Marathon would make it expensive, Red Sox wouldn't.
If he's really into science, the
MIT Museum might be a good stop. Our Museum of Science is good, but not great. I was last there about a year ago, most of the exhibits hadn't changed in over a decade. It's got some great stuff, but it's quite uneven, IMO.
Duck tours are fun, but if he's in to history, the regular Hop On Hop Off buses will actually teach you stuff.
Tons of burger places around. Just drove past
this last night, which is very well located (just off of Newbury Street in Back Bay), and offers a very tasty burger with tons of options, but I'm sure there are a dozen other options or more. Check
here, if you really want advice on food in Boston.
Ask at your hotel (or on that board I just linked to) for recommendations in Chinatown (very close to your hotel) or the North End for best Italian, and how best to get there (subway, cab, etc). There are dozens of good Italian places to eat . . . and a handful that aren't so good.
Whale watching will be very chilly in April, but you are likely to get some good sightings. Not sure what you meant by "itc".
There's a big movie theater in the building the RC is attached to, that will be showing pretty much every wide release open at that time.