I don't know whether you enjoy visiting museums but DC is full of them (almost all part of the Smithsonian complex).
The Holocaust Museum is well worth a visit.
There is also the national zoo, which certainly at the time of my trips over was a good visit. When it is hot they had showers outside which you would just walk through to cool off. I haven't visited in October (my visits were always between January, with snow over a foot deep, and June, when my hair would frizz in the humidity) but I would imagine it will still be fairly warm although the humidity should be low by that time.
The Capitol and old supreme court buildings also worth visiting. The White House is tiny and not worth the effort really although its location comes as a bit of a surprise.
If you like religious buildings there is also a cathedral although coming from Britain you'll be disappointed! It's not exactly York Minster. But they tried.
DC is a beautiful city in the centre but not safe so take care of yourself and your stuff, although having said that it is now 12 years since my last visit (which I snuck in two days before 9/11) and so things may have improved on the safety front.
Pity you weren't visiting in March/April time when the cherry blossom is out and the National Cherry Blossom festival is in full swing as it is truly stunning at that time:
There is a good underground railway system but if you have access to a car a visit into Virginia is worthwhile if you like pretty landscapes and looking at people sitting in rocking chairs on their verandas beside massive pumpkins while holding a rifle in their lap and drinking the local (non-alcoholic) apple cider (well, that's a longstanding impression I have of my time living in Virginia anyway!).
Edited by Saintslass, 28 June 2013 - 12:03 PM.