Low cost nerd places Eastern US?

My fiancé and I are seeking a nerdy destination for our honeymoon, preferably something within a hard day's drive, 800 miles or so, of the east coast of NC in the US. We don't want to spend a fortune because we are not rich, and we are running low on ideas. It doesn't need to be a theme park or anything of a themed nature, because a place with a lot of museums to visit is incredibly attractive to the both of us. We are getting married in a little over a year from the date this is being posted, February of 2024, and neither of us wishes to be popsicles, so it has to have somewhat moderate temperatures at that time of year as well. Please help!!