For beautiful mountains and a stunning coastline my thoughts first turned to
Ireland but I'll assume that you want to go a little further afield.
Liguria a lovely part of Italy, with some delightful small coastal resorts along the beautiful Italian Riviera, such as Rapallo and the billionaire's haven, Portofino. The coastal strip is backed by a range of rugged hills, which offer great hill walking or, for the less adventurous, the chance for leisurely exploration of Cinque Terre. The name means 'the 5 lands' and the area is a National Park and a UNESCO World Heritage Site.
You can find package deals to Liguria but they don't exactly leap out at you from every holiday brochure. That's because, thankfully, the area hasn't been despoiled by massive tourist hotels. You'd need to do some research (or visit a 'proper' travel agency, which actually employs staff who really know about travel).
However, it's easy to arrange you own holiday in the area. Ryanair have dirt cheap flights from Stansted to Genoa. BA's flights from Gatwick are also reasonably priced. (The flight time is only around 2 hours). From Genoa Airport, it's only a few euros for the coach to Genoa rail station (or you can take a taxi - I've done it and it didn't break the bank). The train service from Genoa hugs the coast and it will take you effortlessly (and very cheaply) to resort towns like Rapallo or to the stations which serve Cinque Terre.
http://homepage.sunrise.ch/homepage/avong/cinq ue_terre/index.htm
http://5terre.itgo.com/index.htm
http://www.thomson.co.uk/destinatio