C.S.
I so remember those days!
At that age, even grocery shopping or heading to the mall is a fun activity for the baby. They get to check out the world and other people from the safety of their stroller or the cart, and it will be a nice change of scenery for the both of you. Some malls also have play areas or bookstores with a children's section, and they're great places to head during the hot part of the day in the summer. I think we were at Target at least twice a week at this stage, lol. Along the same lines, a quick trip to the pet store is also fun since baby will love to see and maybe touch the animals.
Some would think since the baby can't read, the library wouldn't be an option, right? Wrong! Your local library probably has some story times and maybe even a small play area in the children's section (I know ours has puzzles, toys, activity tables, and even a small slide).
I agree with the others, joining a MOPS (stands for mothers of preschoolers - but it's from birth+) or local Mother's Club is very fun and beneficial for the baby AND for mommy. You get to meet other moms in the same stage of parenthood and life, and the baby gets to interact with other babies/kids (or just watch and parallel play at this age). As he grows, it will be a great outlet for home playgroups, playground trips, etc... and you both will probably make some great friends.
As far as toys, push toys or simple riding toys (NOT motorized) can entertain them for hours as they're learning to walk and move. My almost-3-year-old still hops on his riding toys every once in awhile. Also, shape sorters or any bucket/container that the baby can put small objects into and then dump out will be popular. My little ones also liked the FP Learn & Groove table and similar (noisy!) toys that they could hold onto and push buttons and all that. They kept their attention until at least 18 months or so. Blocks that can be stacked and knocked over are pretty much universal. When mommy makes a tower, baby can knock it over and clap. Soon, he'll be the one making the towers.
Other simple activities would be bubbles, playing in sand (outside), playing with measuring cups/spoons/pans while you make dinner (the plastic container cupboard is almost always empty at my house because the kids love playing with them), reading books, playing hide & seek or peek-a-boo, etc...
Everything is educational at this age, so just be creative and have fun :) The boredom will pass. He will probably get some new toys for his first birthday, and he will also start exploring more and keep mommy on her toes!