Saimaa Region Home Base: Savonlinna or Lappeenranta?

It's been about 10 years, but I stayed in Inari in July for 4-5 days. It's much farther north than you might want, but I flew back to Helsinki from its airport.
There's a large lake and related activities and the lodge I stayed was right on the river with lots of fishing, at the time owned by a young Sami couple. The museum was excellent and lots of hiking. I did a memorable midnight hike with a guide (I was traveling by myself).
Reindeer clopped around all over!
It wasn't easy to get information as I planned- hopefully you will receive good advice specific to the two towns you requested.

Lappeenranta and Savonlinna are fairly similar, and both are delightful. But Savonlinna has one thing Lappeenranta doesn’t: a huge medieval castle right in the center of town. It’s a breathtaking sight, and unique in Finland. It’s where the Savonlinna Opera Festival takes place in mid-July, so you should avoid Savonlinna then (unless you’re an opera fan).

Transportation-wise, Lappeenranta is easier to get to from Helsinki, in case that’s a consideration.

We were near Savonlinna last summer and also visited Lappeenranta. We enjoyed both. Our accommodation was near Punkaharju, which was an easy drive to Savonlinna. With Finnish friends we rented a house right on the lake, with a jetty and kayaks provided. There was also the essential wood fired sauna and an outdoor kitchen. It was a wonderful base for us. We went to Savonlinna by car several times (approx 30 minutes drive). The castle there was a very interesting and the water front was pleasant. We also enjoyed a visit to the Finnish Forest Museum at Lusto, which was only a short drive from our holiday accommodation. On the way back to Helsinki we visited Lappeenranta. It felt busier than Savonlinna, but there was an excellent market and I remember having a very good lunch on a boat moored in the harbour area.

If I had to choose I'd prefer to be nearer to Savonlinna.