I've been to Mystras and it is indeed lovely.
Beautiful location with many of the churches being restored but everything else is in various states of ruin.
You can park down below and walk uphill and even though there are "lanes" with cobbled stones it's basically mountain climbing and many of the cobblestone paths have eroded over time so it can be a bit tricky. Wear good hiking shoes.
You can take a bus to the top and then walk down hill which will be easier but I liked walking uphill.
I haven't been to Meteora and it does look beautiful but it's a long drive from Nafplio and it will consists of more time driving to/from Meteora than at the site.
Have you considered Ancient Corinth which is very close to Nafplio? Beautiful site and easy to get to and return.
There is a huge selection of accommodations and tavernas in Nafplio so you should have no problem finding something albeit July will be very busy and filled with tourists.
There is a huge amount of archeological/historic sites in and near Nafplio to keep you occupied and thrilled rather than driving long distances even to Mystras.
It sounds like you will be driving from Nafplio to Athens on the same day your flight leaves.
Most experienced travelers recommend getting back to Athens at least one day before your flight in case of any delays or traffic problems along the route.