First thing to know: the number one thing I can recommend for visiting DC is to see the monuments at night. They are open all night, and a park ranger can give you an impromptu tour just by asking, which I highly recommend because they can explain much more than you can just see in your own. Especially amazing at night are the WWII Memorial, The FDR Memorial, and the Air Force Memorial which is in Arlington, VA near the Pentagon. The Korean War Memorial is also fantastic at night. The one monument that is better in the day is the Vietnam Memorial. But all the others are better at night. I also highly recommend visiting the Library of Congress (Main Hall) which is next to the Supreme Court.
The Capitol Hill Hotel is one of the few 'affordable' hotels in DC that will indeed put you within walking distance (depending on how you define that) for a couple of things you want to see. Other distances are vast, but you are near a blue line metro stop which will get you to other places. I live in DC, so I have not stayed at this hotel, but it is in a nice, safe, and desirable location. I recommend that you book early there, and if you find a better deal elsewhere, you can always cancel.
There are quite a few places to eat on Pennsylvania Ave near the hotel with most of them being dreadful. The exceptions will be Good Stuff Eatery (burgers, plus get the toasted marshmallow milkshake) and We the Pizza (also the salads are good here). Both are counter service.