Cab or Uber would be your best bet. Parking is expensive and many of the garages are tight go park and a lot of people don't care so expect dings on your car if you go that route. Not saying it will happen but it could.
As for attractions, Codzilla is pretty fun and so is the duck tour. Super duck tour is the newest one and not the original duck tour. The there's whale watches if you are interested in that and the Aquarium which is pretty fun.
Faneuil hall is nice and a lot usually goes on around there. Quincy market is great for food. Just go in there and check out which restaurant you want to try. I haven't had a negative experience in there in the past 10+years. There's all kinds of food and good lobster too.
North end, or as we call it, little Italy, has TONs of restaurants and bakery's. All are really good and again, nothing but positive experience from me. Mike's Pastry is a popular one but I avoid it since there are tons of other bakery's around that area that are great but without the crowd. Just don't go to any chain restaurants over there.
Faneuil hall, aquarium, little italy, and the Boston harbor are all walking distance so that's why I said to Uber it. I don't use Airbnb so I really can suggest where to stay. Tell us what you find and we can go from there.
Seaport is a bit pricey for restaurants like Del Frisco's but it's good. There's also Jery Remys which is really good and average price. But parking in the garage is $40 and you get a good view of the harbor. That's about a 20-30 min walk from Faneuil Hall.
Boston Commons is a nice relaxing place. Not as nice as NYC Central Park but I like it a lot. And I do go there whenever I have time to just relax for a few hours.
I also know a lot of tourist wants to check out Cheers but as someone who have lived here, I have never been there. Not my interest.
Charlestown Navy Yard is where I go a good photo of Boston skyline. If you walk behind the Aquarium. You can get some good shots of Boston as well. Sorrow drive is also another nice place to go but parking is not easy there.
Hope this helps.