Must Visit Places

I’m taking my first trip alone to Richmond in a few days and will be there for 2.5 weeks, visiting my cousin, so looking for suggestions for things to do/places to check out! It's my first time up in the southeast or anywhere up from the deep south honestly. I'm also wondering if other popular places are 'close' to where I can take a train or bus? I was thinking of maybe visiting DC by Amtrak or is bus cheaper? Is there days were the fare is cheap for amtrak?