As most people work for gov and contractors, lots of work from home due to telework.  

I'd do Tyson's, Arlington, crystal City, etc.  

Would avoid the metro at all costs due to crowds and just service is unpredictable these days. Find a place and pop a squat until you absolutely have to leave.

I have been to, and done a number of inaugurations, yes, I'm old.

Friday the 20th is a Federal holiday, and many companies tell people to work from home.  That being said, getting around DC will be very difficult the morning of the inauguration.  Getting into town will be crowded, but manageable since people will 'trickle' into town.  The madness is after the inauguration when 100s of thousands of people disperse simultaneously.

The inaugural balls themselves, if its your first time, it is exciting and fun.  After your first one, you'll probably not want to go again.  The "food" will run out fairly quickly if its an official ball, you'll wait forever for your coat since they'll only hire a couple coat check girls to help, and hopefully you won't lose your coat.  You'll be standing around a lot, and if its not an official ball, you probably won't see the President.  If it is an official ball, you'll probably only see a glimpse of the President.

If you are going to the inauguration, its not formal and dress really really warm.  I've walked back from the mall to Crystal City before because the metro was packed - and it was actually an easy and pleasant walk back, its just across the 14th street bridge.

You will find Hotels in DC non-existent or very expensive.  If you're 'working' I would consider parking yourself in Tyson's Corner.  The day of the inaugural ball, would get closer-in if possible just for convenience of getting in-and-out of the city.  If the ball is at National Harbor, makes it much easier IMHO.  

Have fun and enjoy, sounds like its your first inaugural.  Its exciting and a lot of fun and just ignore me, I'm a jaded old curmudgeon.  :