Looking at a short trip in mid may to DC, mainly to visit the Smithsonian Air and Space museum, Natural History Museum, and just site see some of the monuments and such. Hotel prices in downtown near the museums are insane. Where is the easiest place to get a (relatively) reasonably priced hotel and be able to easily get to the museums and mall area via uber or mass transit without getting mugged? Would love to be under $300/night, but mainly just not interested in paying $500+ per night.

Also, how hard is it to get to downtown DC from the Baltimore airport? Is there a metrorail line or bus service that is easy to use and relatively safe?

Stay in Crystal City or Rosslyn across the River in Virginia and the hotel options will be plentiful and cheaper and you will be an easy Metro ride (subway) from the museums and downtown DC.

There are trains from BWI to Union Station. You can then transfer to the Metro to get to your hotel. MARC trains are cheaper. Amtrak trains are nicer and faster.

I've been staying at the Hilton Key as of late for all of my work trips. Great location, 2 blocks from the Roslyn metro and walkable/short uber to Georgetown restaurants/bars across the bridge. Brand new hotel (less than a year old I believe). I've gotten upgraded to the 1 bedroom suite overlooking the Potomac with views of the Washington monument and Capitol building off in the distance 2/3 last stays I've been there.

https://www.hilton.com/en/hotels/dcarthh-hilton-arlington-rosslyn-the-key/