For more certain weather I'd go for early June, although early May could well be lovely weather. Days are a bit longer and a few degrees warmer. A detailed run-down of the likely weather is here
http://www.agni.gr/guides/weather/weather.asp

Paleokastritsa has some lovely views and walks (it's not flat), and three beaches. Probably about 30 mins transfer by taxi
http://www.agni.gr/guides/resort_guide/paleokastritsa.asp

I've stayed in Arillas, which is not very lively - a number of tavernas and a couple of bars, but nice for a chill-out, and not a McDonald's in sight. It has a pleasant beach. It depends what you like I guess
http://www.agni.gr/guides/resort_guide/arillas.asp

Check out some of the other resorts, there are some nearer the airport, e.g. Gouvia.

I can also recommend the north-west coast villages of Arillas, Agios Stefanos and Agios Georgios north for a quiet restful few days in beautiful countryside and among friendly local people. All are about 45 minutes by taxi from the port.
The first 2 have more active resort centres and are slightly busier than Agios Georgios north but all would suit couples in their 50s.
http://www.sanstefanos.co.uk
http://www.arillas.com
http://www.agiosgeorgios.info

I know Agios Georgios best and for independent bookings I can recommend the apartments where we stay:
http://www.yiannisplace.com. They are surrounded by lovely quiet gardens and are about 10 minutes walk from the beach.
If you prefer a hotel the Belle Helene Hotel can be booked independently.

As already stated early May weather is more varied but we have had some lovely weeks then (and some mixed ones in early June). The May countryside is really fresh with many wild flowers but one problem for some people is that the tourist trade has not really got going so some tavernas may not open until mid-May. It is my favourite time to visit Corfu but early June is a close 2nd.