I did a little poking around on rates and locations...not knowing when you plan to come, but assuming it might be soon! Alexandria has more plentiful selection of hotels of all budget ranges. It is Summer, but maybe since school is not yet out hotels are showing discounts as they normally increase in the summer.
Finding a hotel in the $100 range is going to be difficult as taxes and parking can lift your nightly rate past $150 range. Given your budget, I noticed some 3rd night free sales here on TA, so they may be worthy of doing a little research. Old Town is my specialty, and I noticed more than a few hotels that normally sell for $250+ that have some specials. They are in the zip code 22314 area also known as historic district. This area is problematic due to added charges for parking $30/night. There are some hotels along Eisenhower Avenue that are walking distance to the Metro that do not charge parking, so have a look there.
I'm thinking, given your criteria the best place for you is near the 6000 block of Richmond Highway aka Route 1. There are a number of decent/new/clean hotels (Red Roof Inn/Holliday Inn Express/Days Inn/Hampton Inn) that are in a safe neighborhood, free parking and ....conceivable walking distance (or via shuttle) to metro. Metro is approx 1 1/2 mile and is probably worth driving and paying daily parking rate. This is the area I would concentrate for your stay. The zip code area is 22303 and is alternately titled Alexandria/Ft. Belvoir/Mt. Vernon/Huntington. Note, it is NOT really near Ft. Belvoir/Mt. Vernon (6-8 miles).
I hope this gives you a starting point. Write back when you have narrowed and I'm happy to weigh in!
I hope this is helpful.