Weather in late April/early May can range from highs 70-85, lows 40s-mid 50s. Generally very pleasant, possibly humid, with cooler nights. Average last frost date is April 15. Past the worst of spring tornado season, which is late March/early April. You will definitely want AC to cool off in the daytime but nights will probably be comfortable.
It's a very pretty time of year. You could come much earlier for peak spring wildflower season and much more variable weather. But late April will be super-green and lush.
So far as attractions, it depends on what you like. There is tons of historical stuff, including major Civil War battlefields, wonderful natural beauty, and a highly varied music scene. Check out TripAdvisor.com to get a good idea of what is available. Tennessee has one of the best state park systems in the country, but it is heavily used so book early if you want to stay at one.
There is a COE campground--Seven Points--about 20 minutes from downtown that is highly recommended. Many beautiful state parks within an hour, just google "Tennessee State Parks" or check rvparkreviews for details.
Single empty-nester in Middle TN, sometimes with a friend or grandchild on board