Most of what you find on TripAdvisor is probably from before the Silver Line was running. Now, Tysons and Reston might be different, but as a rule, I'd imagine you could find a hotel with a shuttle to the Metro for cheaper out west than closer in by Arlington. Similarly, along the Blue Line, it's cheaper farther out by Alexandria than in by Crystal City.
Yeah, you'll pay a bit more in fares (about $3/person roundtrip for Reston vs. Crystal City). But for a family of five, that's equal to a $15 difference in room rates. Arlington has better dinner options, but I'd probably eat in the city anyway. If it were me, I'd probably buy five weekly passes anyway. That way, you get unlimited rides for the days you're downtown. Most of the destinations you've mentioned can be walked fairly easily from one another, with the exception of the Zoo and the National Cemetary, which will take their own Metro ride. But you'd have more options for lunches and dinners (and shopping if that's your thing).