Your post seems to shout 'Italian Riviera' to me.
Ryanair fly from Stansted to Genoa. Sample fares, per person (including all taxes and charges but excluding booking fees, checked baggage fees and priority boarding charges) are as follows:
Out Monday 03/08 (at 0950, landing at 1255): �19.99
Back Monday 17/08 (at 1320, landing at 1325): �14.99
http://www.ryanair.com/site/EN/
It's an easy drive from Genoa Airport to such delightful little resorts as Rapallo. These firms provide car hire facilities at the airport:
http://www.airport.genova.it/v2/index.php?opti on=com_content&view=article&id=68&Itemid=137
Rapallo, and neighbouring resorts (such as Santa Margherita which was beloved by Liz Taylor & Richard Burton) are quiet and fairly 'classy' without being expensive. (The only exception is the billionaire's resort of Portofino which is worth a visit but is definitely way beyond the means of 'mere mortals'!). There are good, sandy (but small) beaches which, like nearly all Italian resorts, are dominated by 'beach clubs' but with plenty of 'free access' areas as well.
Places to walk? You're right next to the Cinque Terre National Park (which is a Unesco World Heritage Site).
History? Genoa has a fascinating 'old town' area, packed with surprises around every corner.
And if you fancy sampling the superb local wines on your travels you can forget the car and use the cheap & frequent coastal rail service.
Googling 'villa rapallo', 'villa italian riviera' or 'villa liguria' will find plenty of reasonably-priced offers of accommodation.
Chris