Seeking Activity/lessons Suggestions for a 3 and a Half Year Old?

I signed mine up for baseball (teeball) and soccer at 3 1/2 even though it said 4. They didn't mind... You could try a toddler tumbling/gymnastics class.

Does your area have honk ball? In TX there was honk ball for 2-3 year olds (basically, it's Tball for very young kids, and they run to the base and jump on it, it honks, the kids think it's fun and will actually go to bases that way). Soccertots, if you have that, starts at age 18 months. Some marital arts studios are 4 years old (my 4 year old already has his yellow belt in kung fu, though they don't start sparring until age 6). If you don't have him in preschool, perhaps taking him to a summer daycamp? I know that pretty much every daycare or preschool in the area we used to live had a daycamp with a specific theme for the summer and that way he could get some fun with peers, but it could be just a half day program or whole day, depending on your preferences. Is there a young chef academy or a place that would be fun to learn another language?
For sure there is gymboree (they offer plenty of fun activities either for kids alone, or mommy and me classes), little gym, and some gymnastics places start at 2 years old but for real basic stuff. My son was 2 when we put him in gymnastics, though you have to be with him to assist the teacher. He loved learning to balance on little beams (like inches from the floor), flips, balance games, jumping on the trampolene stuff, and swinging on a rope into a pit of big foam blocks. Kindermusic is actually really sweet, we love that. (I did it with my oldest, and am now doing it with my 1 year old). They both are in swim lessons every summer: lots of swim lesson opportunities...I don't know names around you, but Emler, Aquakids, Aquatots, YMCA, any local rec center I would expect. I would suggest you check out the free parenting magazines in your community (usually at a doctor's office or grocery store, something like a Fort Worth Child or Suburban Parent), where there will be loads of advertisements for opportunities, services, special events, etc in your area. That's how I found out about birthday party options, horseback riding lessons (a 4 year old friend does this), swim lessons, but also lots of special events to get customers in at different places.....like a pottery place might have a special kids day where they'll offer a deal or free ceramic and you just pay for the time slot to decorate it, etc. Some museums offer little art classes. There could be a play center near you that has bounce houses, dress up, games, train tables, etc that you could do on bad weather days. Lots of picnics, trips to the botanical gardens that include picnics and some time with a ball. I would also suggest joining either a moms club or early childhood pta (ECPTA) because you can have some adult time but also get in on some great activities you may not know exist around you, and most often for a discount.
Things my son(s) were/are involved in over the years (oldest is 4, youngest is 1): kindermusic, gymboree, tumbling (baby gymnastics), storytime at the library that also involved a craft or singing, small fry club at a local McDonalds where once/week we'd meet in their indoor playland for a story, game, craft, sometimes a special guest like Ronald McDonald, the firefighters, etc....this was nice b/c we moms would help with the craft, then the kids would play in the playland while we chatted, and we'd grab lunch there. We also did honkball, soccer tots, and the children's museum. Summer movies at the theaters were free or $3 depending on where you went (a special morning showing of a kids' movie). We went to lots of museums especially cowboy stuff. Now the oldest is in preschool, kung fu, awanas (a church club that's kind of a very young boyscouts meets vacation Bible school kind of thing), and soccer while the youngest does kindermusic with me and storytime at the library. We've done swim lessons for both boys starting at 10 months old, every year. Local flavor (Fort Worth had the stockyards where you got to see cowboys, ride a mechanical bull, watch a rodeo, sit on a real long horn steer, watch them herd the long horns through the street and gun fight shows, ride a horse and buggy, etc....find what the local "thing" is where you are, or nearby, and go with it). Now we've moved to the east coast and do the beach to fly a kite, picnic, search for sand dollars and horseshoe crabs, build sand castles, make "sand angels", play soccer on the beach, tour lighthouses or whatever. Looking forward to it warming it a little more and playing in the water. EVERYTHING you do can be educational AND fun if you want it to be. We go giant hunting in the nature preserves but while doing that, we take time to hear the wind blow through the trees and watch the wind pattern as it moves the trees around us, we learn names of trees and plants, we see what different tracks/footprints are and even inspect "poop" to see what animal has been there. (Yeah...they're boys. That rocks their world). Almost everything we do is free, by the way.
Another thing we do weekly is go to the farmer's market. I let them pick out one new thing we've not really dealt with before and we figure out something to do with it that week. Last week we got yellow squash (as a kid I didn't like it, but maybe just b/c it was this same dish that I didn't like)....the boys picked it out, so we cooked ricotta gnocchi (pre-made, from someone at the market) with spaghetti sauce and some fresh vegetables added in, including the squash. Go figure, it was delicious. Another time, we got a neat idea from that market and together made a crepe with fresh spinach, mushrooms, goat cheese, and roasted peppers and a dessert crepe of nutella, cream, and fresh strawberries that we all shared as a family. The baby sits in his high chair and smashes things for me and the 4 yr old "helps" by pouring measured ingredients into the bowl and stirring, etc. They like to learn cooking. We met some people at a farmers market that had an organic farm and grass fed beef nearby; we asked and scheduled a trip to see the farm and take a tour, they taught us about where our food comes from and that was cool. (They were most impressed with the tractors though). You can also request tours at different places, especially if you can get some friends together and make it worth their time....I've been on tours of Mrs Bairds, a pizza place, a bottling company, the mint where they make money, and a candy factory with my boys. We've also arranged with the fire station for a tour, and we made brownies; my son, when he was 2, helped make them and then helped wrap them up, and we took them to the firefighters to thank them for helping our community and keeping us all safe, then we got to tour the station and firetrucks. Do you have trains, subways, trolleys, an airport, etc around? My boys liked riding the bus around the airport and we'd get off in one location, walk a little bit, see the planes, catch another bus, etc. Easy to do with a stroller and older one, as long as the older one will keep a hand on the stroller so you're not having to chase. We used to sit at an observation park and throw or kick a ball around in between planes landing VERY close, and that was fun. It's a wonderful age actually, because SO MUCH is new, and very impressive, to that age! Have fun!

music like kindermusik or music together
should be plenty of swimming lessons for his age??
gymnastics
dance
soccer (pee-wee)
t-ball

Dance classes. good for both boys and girls at that age. And imagine how cute he'd be doing a hiphop number!!! tee hee... :)

Like JC A said, try the YMCA. Also, try the Part District. Ours has a couple of really good options.

if you have a YMCA near-by they have a lot of different stuff that you can do with him. My little guy loves gym class and swimming classes there.

You could also check to see if you guys have Little Gyms close to you.

I don't know if you were looking for more organized classes or what, but those two are great in our area!

Soccer usually starts at 3 and it is a great sport for kids to play. My first son started at 3 and my younger son can't wait to start in August after he turns 3.

Swimming definitely starts younger. My local YMCA has classes starting at 6 months! Also try art, music, gymnastics, dance, language classes.

My county's nature center (FYI, I'm in Essex County, NJ) has nature classes for 18 months and up.

Karate schools do not typically start kids that young.
My daughter takes Karate. At her Dojo, they do not allow kids to start until 5 years old.

Baseball at this age is not baseball. It is T-ball. Again, they may not start kids this young.

Soccer. Some groups do have "toddler soccer." So you might want to explore that.

Swimming: they do have classes for kids this age. For "Toddlers."