I definitely would recommend a trip to visit Mystras. It is an old town on a big hill with lots of great old churches and buildings. When we visited the palace was closed for renovations but it still took us a half day to see the entire site ( 9:00 AM to about 2:00 PM).
The churches have amazing wall paintings that are the original works and the site over all is really pretty, very steep with many winding paths and of course when we visited lots of wild flowers.
We arrived in town on orthodox Easter Sunday so finding accommodations was pretty hard. Many of the businesses were closed and all the hotels were booked full. We ended up in Sparti which is a short drive but I think we got the last hotel room in town.
If you plan to travel in Greece around orthodox Easter make advanced arrangements. We stopped in a few places to find a hotel and everything was totally booked since that is a four day weekend for many Greeks. Also all the museums and sites are likely closed. The way it worked when we visited is that on Easter Sunday all sites were closed, on Easter Monday they were open but the following day, Tuesday all the sites were closed.
We had planned to visit Ancient Messini on Tuesday but as I mentioned it was closed. Honestly after our big hike at an amazing site (Mystras) Ancient Missini didn’t seem as spectacular except for the “drive through” ruins which are on the way.