If you are in Barmouth, you won't find better than the Rhinogs, from Barmouth to Trawsfynnedd there is eveything there to keep you amused for a week, exploring the whole range of hills (in your own time). Have a look at the section of Meirionnydd round route perhaps, finding all the tops will test your navigation skills and be rewarding.
http://www.gofar.eclipse.co.uk/meirionnyddround.html
You will need OS Explorer OL18 1:25K you'll want 1:25 scale to navigate up there
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In fact I love it so much I am packing my sack this evening and heading for Barmouth tomorrow morning, will head North on the route and bivvy (no tent) under the stars tomorrow night somewhere on North end and return Saturday. Just poking about and enjoying the hills.