If you're flying into Pisa Galileo Galilei Airport there's a direct train service to Pisa Central station. From there you can catch a train northwards (with a reasonably frequent service, and a journey time of around 1 hour 40 minutes) to the lovely little coastal town of Rapallo. It's big enough to have a lively market but small enough not to be packed with overseas tourists. (It's where the smart Italians go on holiday!). It's got a small but pleasant sandy beach, looking out onto a stunning bay (which you can view from the patios of the good quality bars and restaurants across the road).
Rapallo is a great base for exploring. The (really cheap trains) take you to Genoa (with a beautiful old city centre) or to nearby resorts like Santa Margherita (still famous for its associations with Richard Burton & Elizabeth Taylor) or into the (World Heritage Area of) Cinque Terre. Or you can take a boat (because no cars are allowed) to the billionaires' resort of Portofino (or to further afield if you want).
I love Rapallo so much that I've visited it several times on day trips(!) from the UK! (I've used Genoa's Cristoforo Colombo Airport, to approach Rapallo from the north)
Self-catering accommodation is in limited supply in the area but there are a few possibilities. e.g:
http://www.tripadviso..._Italian_Riviera.html
Unless you've won the lottery though, it might be best to avoid Portofino!
http://www.tripadviso..._Italian_Riviera.html
Chris