I’ll contradict gunna and say take the CX bike. There is not a lot of decent, joined up, legal riding local to newquay – the locals can string a good ride together, but you’ll struggle. There is however loads of family/tourist trails and country lanes that make for a very nice ride. No big hills, but no flat bits either.
From Newquay I’d ride up the coast to Padstow, then turn back inland and ride though St Wenn on the way home. If you want to go further take the camel trail all the way (you lose the bike hire people after wadebridge) to Blisland up on the moor and then back through the lanes.
Or head to here. Family trails with the odd offshoot that will test a CX bike and lots of picturesque vistas, plus tea & cake!
http://www.cornwallcyclehire.com/