You can get a package from tour operators to Finikounda so you may be able to grab a good deal. Transfers from Kalamata are around an hour an a half.
Finikounda, where my wife and I had our honeymoon in 2013, was our first introduction to The Peloponnese. The place had a nice vibe and, despite being tourist orientated, it still maintained a fishing village feel. We stayed three weeks and really enjoyed our time there. The beaches and restaurants were good. We hired a car and explored the region, discovering Koroni, Methoni, Polilimnio and Ancient Messene. Finikounda is in an ideal location to do this.
We also visited places farther away such as Olympia, Nafplio, Lousios Gorge and our first foray into The Mani. Finikounda is definitely not so well situated to visit these places as the roads can be slow but we do not like just like to laze around all day every day, [well not every day].
We discovered the beach to the south [or is it East?]. I think it was called Sabbia beach. To find it turn left when you reach the seafront in Finikounda and keep going until the main beach stops. You then have to scramble across some rocks with the help of some planks which was fun or you could head inland and enter from the rear [ooer]. There was a lovely Taverna there and sunbeds. It was quieter here than the main beach and we loved it.
The main road passes by the main resort which is a good thing. We stayed at the Panorama Aparthotel which has two pools and the room was fine. It is set back from the resort meaning that we had to cross the main road into the resort proper, but we did not mind the pleasant ten minute stroll.
In 2018 we thought we would revisit Finikounda for nostalgic reasons and stayed a night at Hotel Korakis Beach which was pleasant. It was lovely reminding ourselves of our honeymoon and the main street did come to life at night just how we remembered [in a low key way], however we did think that the restaurants were more expensive than in Stoupa. Sadly, our favourite beach had been abandoned it seemed. The taverna was gone leaving just an empty shell. I guess that it was just too quiet for the taverna to keep going, a real shame. We revisited the restaurant Elena which has great views over the bay and it was a good meal. You pay a little extra for the view, but it’s worth it.
2022 UPDATE– The beach is up and running again -YAY! The taverna is called Lemon Drops Bar and gets great reviews- [Thank you to Alison Saunders for this info].
In summary, there is no real reason to visit Finikounda [apart from the sun, sea and sand] unless you are staying here but it’s a good base for exploring the rest of Messinia.