We have stayed at: (in order of preference)
1. Park Vue Inn (X3): Is literally across the street. Close enough to head back to your room for lunch or a nap. The layout of the bunk bed rooms is awesome as well. The breakfast is STELLAR and there is no better way to get psyched up about your day than to eat your waffles facing the Matterhorn! And that is not taking into account the little things: Welcome basket in your room upon check-in, cookies in the lobby, etc. I would stay here again without hesitation!
2. Portofino Inn- (X1) LOVED the kids' suite. They pull it off brilliantly! And the IHOP on this corner is WAYYYY better than the IHOP across the street from the walkway. But it was a bit pricey, and no breakfast options.
3. Candy Cane Inn (x1) I know this place has a Ron Paul- like following on the internet (and I don't mean that politically, I mean it in the fervor and devotion of supporters.

) but we were very eh about it. Yes, it is close, yes, it is a very "ma and pa" type feel, yes it has a dedicated shuttle. BUT...the rooms are teeny teeny tiny- and we had the "deluxe" room. Motel 6 sized tiny hotel room. The breakfast is danishes and donuts, and the only place to eat is on the pool chairs which are still soaking wet with morning dew. And the dedicated shuttle takes a 2 hour dinner break, with no notice listed in any of the hotel information. We found that out after we gave up waiting and we gave up an walked back.
4. LaQuinta Inn (X3) Farther than a block away, but the price is great- Under $100 for a kids suite! But the last time we stayed there the hotel was not as well kept as it had been on our previous visits so I don't know if I would want to stay there again.
Also, make sure to Google map what a "block" is when you are considering where to stay. For instance, the Candy Cane Inn and Portofino are indeed "a block away" from the entrance, but that block is the entire length of DCA.