As first-time visitors, I'd assume that you are interested in checking out The Mall (Capitol, White House, museums & galleries), a waterfrontfront view (probably you're thinking of a walk-followed-by-dinner in Georgetown), and maybe sight(s) in Northern Virginia just over the water like Iwo Jima, or the 9/11 Memorial at the Pentagon, etc.? If you want the whole visit to be a DC experience, you should stay in DC - and if you're willing to walk a lot (which is really how you'll get the most out of DC as a tourist), you can find reasonably priced options in DC. OK hotels will be anything 3 stars or up on review sites - maybe recognizable names, 3+ stars, independent names, 4+ would be a good rule of thumb. If you're driving, the short answer is that it's worth it to stay in *Maryland* instead of Virginia, for navigation reasons, unless you have plans in Virginia or someone in your group is very good with directions and wayfinding. I know Virginia to DC looks like Allston to Boston, but it's organized radically differently and easy to end up stuck and lost, whereas Maryland is more of a blended transition and the roads from DC are more accessible to the uninitiated. I can't speak to the hotel prices, but I can offer you some parameters. If you plan not to drive, try to stay on the subway's Red line or Orange/Blue line. Buses are OK, but only reliable on arterial roads or the DC Circulator. Check out these neighborhoods for convenience and because they'll have moderately-priced options (I'm adding places with ... that you can expand to if you'll be driving):
Friendship Heights is the more expensive area, and is the DC-MD line. Wisconsin Avenue is a major artery into DC (it terminates in Georgetown) and a good scenic drive for the Cathedral, Dupont Circle (from where you can find Watergate and the Kennedy Center) and Georgetown. It feels like DC, there's good eating from here to Tenleytown, or you can walk through a pleasant neighborhood to Connecticut Ave for even more options.
Bethesda had a lot of hotels and is 1 Red Metro line stop or 10 minutes drive further up Wisconsin. Pretty quiet at night but a burgeoning dining/brunch place (DC brunch is a thing, even with Covid).
Rockville is 10 minutes further up the road and encompasses 2+ Metro stops. Wisconsin Ave turns into Rockville Pike; both are called 355.
Rosslyn (Virginia) ... Courthouse, Clarendon, Virginia Square, Ballston
Rosslyn may be pricier, but you will be in walking distance to Iwo Jima [don't miss the Carillon as well as the unmissable view of downtown DC from this hilltop]. It is also just across the bridge from Georgetown. All of these neighborhood stops are in Arlington, VA and on the Orange/Silver Metro lines. The further you go, the more you'll feel like you're staying in a different town and commuting to tour DC. However, the direct drive/Metro into the National Mall can't be beat if you plan to spend most of your time there.
Dupont Circle/Foggy Bottom (DC)
You won't be downtown-downtown, but you'll be in one of the lively and scenic areas of DC; these choices offer walkable options for good restaurants, nightlife, Georgetown, Watergate & Kennedy Center.
Even though they are on different Metro lines, the reality is that these places are next to each other (the walk from one stop to another is about 10-15 minutes). Similarly, nearby Farragut North and Farragut West are also easily walkable (both line Farragut Square, a park block). Expect other Metro stops to pretty reasonably farther away. From my memory, the T stops are also pretty far apart, so it's kinda the same. The Metro is dealing with issues, so be prepared for delays and don't rely on the schedule so much. Taxis are fine and there are a bunch of different colors of vehicles - any official one has a light on top.
Sorry I can't give you specific "best hotels," but hopefully this gives you enough insider information to make a better-informed decision.
Kelly Thank you so much for all the incredible information! I really appreciate it.