when I worked in town we used to go to alot of these places and alot of other places but you requested the more budget friendly places so I didn't include the others.
For drop bottom price I'd say
No Name restaurant. I haven't been in years but it used to be a good inexpensive fry (fried Fish) shop.
I know there is a sushi place out on the piers also that's supposed to be very reasonable priced but I've never been you may be able to google it.
For chowder I'd go either Chowder House in the food court in faneuil hall or the Union Oyster house around the corner.
I honestly think Union Oyster house has great seafood at extremely reasonable prices and its a very historical restaurant (oldest continuously run restaurant in the country and where toothpicks were first introduced to general public.)
Wagamama for fun japanese cafateria style dinning.
I also recommend checking out groupon and buywithme. Both sites offer good deals on a lot of local restaurants.
If you don't want to buy into a long harbor cruise boston harbor cruises does a lunch cruise for I think 12 bucks.
Also if your coming during
restaurant week you could make out like a bandit.
Overall your best deals are to be had at alot of smaller mom and pop shop style restaurants.
In Downtown there is a great sandwich joint called
chacarero.
There are a ton of lunch spots in the financial district:
Sultans Kitchen
zo
You could also head to chinatown for a large selection of authentic cantonese vietnamese, japanese and thai foods. If your a little adventurous you'll find amazing food and deals in chinatown.
Also visit the visitor information center on the boston common its where the freedom trail starts and everyone who works there is from the local area and they eat in the area so I'm sure they could give you some great suggestions.
If you do go to cheers only do so for their bloody mary's otherwise skip them the interior is not what you think of when you watched the show. Just take a picture outside. Skip legal seafood its over-hyped. Try the pickles from the pickle guy in the boston common there actually good my niece made me try one once. In the North end stop by mikes pastry the lines there for a reason and if you want a huge inexpensive italian sandwich go to Bovas Bakery. I honestly can't think of alot else but there is alot to be found check out Phantom gourmet and yelp for more options/reviews and have fun when you get here.
