If there is a fun playground next to the gazebo, I wouldn't really worry so much about games. I had several birthday parties for my kids at parks (& that's how you do it in the south from spring through fall) & all the kids really wanted to do was to play on the playground & eat & then go back to the playground. It makes it really inexpensive, because all you have to do is provide the cake & punch & goody bags. However, if you do want to plan some games, I've successfully ran these "races" a lot of times with all ages at the same time -- the kids love them & you can give out little prizes, or better yet, ribbons:
Lollipop Race: Get a bag of lollypops that have string for the handles, not sticks, or, if you can't find those, some other bright colored candy or little toy that's wrapped (so that they don't know what they're getting). Spread the lollypops out in a line about 50 feet or so from your starting line (I always used a long rope or even yellow yarn for my starting line). When you say "GO" the kids have to run down to the lollypops & grab one & run back to the starting line. They're prize is the lollypop! Another bonus -- it's such a kick to see some of the little kids run down as fast as they can & then spend a couple of minutes choosing the color of lollypop!) At this point they can take a break & eat the lollypop, if they want. (You can get sugar-free lollypops with strings, if you're worried about the sugar, or another idea if you make little goody bags, is to put them at the line instead of the lollypops.) If you do that, I would run this race last.
2. Jump the Brook: this is another favorite that can go on & on if you let it or need it to. Make your brook with your starting line rope. Have 2 parents hold the rope at either end on the ground (or you can use older kids who don't at the moment want to participate, although at some point, they usually end up getting into the act). For your other side of the brook, stretch another rope about 1 foot away from the starting line (it helps to have 2 more people to hold this rope, too). The kids line up & run & jump over the brook. After the kid jumps over the brook they run around & get back in line. When it's the first kid's turn again, move the rope about 6" further away from the starting rope. Continue to move the rope in increments of about 3 to 6 inches after each rotation. If a kid lands in the "brook" he's out (if you so choose.) Sometimes with little kids, they don't understand that they're out, & go back around to jump again & that's OK, too! It's great fun & the kids love jumping! I've use jump ropes for my brook edges because they don't actually need to be very long -- the kids should stay in a single line & wait until the kid before him has moved out of the way before starting to run. You can also use a chalk line, if you have access to chalk, for the starting line.
3. Sack race: You can get gunny sacks or old pillow cases & have the kids jump in them to the finish line (again about 50 feet or whatever you think from that starting line.
4. Egg in spoon race: I liked to use big marshmallows & plastic spoons. Little kids can hold the spoon by the end of the spoon (not the bowl end & race (slowly) to the finish line. We've done it with big kids having to go back & start over if they drop the marshmallow, but the little kids can just pick it up from where they dropped it & put it back on the spoon. Only rule is they can't hold onto the marshmallow at all while they're racing.
5. Obstacle course. For this you need all of the parents, I always at that age required my parents to stay, & they always wanted to, anyway. Have 3 or 4 columns of 3 or 4 parents or older siblings in each column (it depends on how many parents/older siblings you have as to how many columns you can run at the same time). The first parent in each column stands about 20 feet down towards the finish line which legs apart -- the kids have to go thru the legs of this "obstacle". The next person squats down about 10-15 feet further on so that the kids have to "leap-frog" over the back of that "obstacle". For the little kids have the "obstacle" get down as small as possible on their knees (tuck head in, too). It helps to use smaller people for this. For the bigger kids (8 & up) the obstacle can be bigger people (dads) or make a bigger obstacle, but the kids should still be able to "leap" over. The 3rd person is at the end & the kids have to run around (or for the bigger kids, run 1-1/2 times around) the "obstacle", then the kids run back to the starting line. Then the next group of kids starts. If you have enough parents, you can put in another "obstacle" inbetween the 2nd & last, with a soccer ball that the kid has to dribble around (by kicking). I wouldn't have more than 4 columns though. It just seems to work better to run 4 kids at a time & you can give 1st thru 4th place ribbons to each flight of kids. (Or run 3 colums & give 1st thru 3rd).
6. Galloping or skipping race: depending on the kid's abilities. I've also used stick horses (I've made them out of a 2 foot long, 3/4" to 1" diameter dowel & attached a stuffed sock (mens white tube sock, black or brown work great). Glue on some button eyes, yarn for hair & pull up a bit of the sock in a couple of places & tie thread or sew around it to make ears, & glue on a big red felt mouth. You can stuff the head with cotton batting from the craft store, or even with newspaper or paper towel (batting works best) & glue &/or duct tape the end of the sock onto the stick. The kids love to gallop -- even the big kids. You can even have them gallop around "obstacles" (again, parents) like in barrel racing, or if you have cones, or other obstacles that works, too. If you don't do stick horses, just galloping or if they've learned to skip, have them do that to the finish line & back.
Note: I've made "Ribbons" out of 1" to 1.5" wide grosgrain or satin ribbon & written stuff on it with fabric paint markers (experiment first, because some of them run. Permanent markers also tend to run. Gold or Silver paint markers work well) The kids LOVE to get ribbons. You can also buy them at party stores, US Toys, Oriental trading or trophy shops, but I liked making them. If you make them, you can just get different colors (blue, red, white, yellow, pink, green, purple, etc. & write "your daughter's name" Birthday Party & the name of the race on it & the date. Cut one end in a chevron, to prevent fraying, & fold the other end down about 1/2 inch & fasten with a safety pin. If you have pinking shears (zigzag scissors that will cut fabric) you don't even have to cut the chevron or fold down the top. I usually make my ribbons about 4 inches long & use 3/4" to 1" wide ribbon, although, you can also use narrower ribbon & not write anything on them. It all depends on how much time you want to spend on it. Kids LOVE wearing ribbons & I've seen little kids try to get one of every color. I've also put on a lot of childrens games for various Scottish & Irish festivals, Cub Scouts & Girl Scouts over the 30 years of my kids. These are the most fun games & most inexpensive. Everyone enjoys them, & all of the kids can get ribbons in each race so they've all won something.
Two last "games" are "Duck, Duck, Goose", which is fun to play, & of course a piñata is always fun.
Hope this helps! Have fun!!!