Late spring is a beautiful time to visit. Just make sure that you don't pick a commencement weekend. You probably know about all of the colleges in Boston and Cambridge. Commencement weekends the hotels will be super expensive and likely booked, and it's impossible to get a decent dinner reservation.
The duck tour is a lot of fun, I would recommend it. As long as you don't mind the walking, the Freedom Trail is very worthwhile. Guided tours are available, or you can do it yourself--you just follow the red line painted on the sidewalk. You'll end up at the USS Constitution.
The Boston Museum of Fine Arts is excellent, as is the neighboring Isabella Stewart Gardner Museum. If you are coming late spring, and you go to these museums, you might also want to go for a walk in the Fens--there is a beautiful rose garden there which may be blooming during your visit.
For Italian food at $25 and under, in Boston's North End I would recommend Pomodoro (for pretty much anything), or Daily Catch (famous for their squid ink pasta, I like their clam sauce), and Modern Pastry for dessert (cannoli).
If you are planning to see a theater performance, an Italian restaurant in the theater district that might fit your price point is Teatro. It would be pushing the upper limit, but you could do it if ordering carefully. Their antipasto for two is very, very good.
I'll give some thought to hotels, and post again later. if you have any specific questions or want suggestions for particular activities or locations, let me know.