Shane, not sure how bike fit you are, when I was 15 I road from Chippenham (just down the road from you) to Melrose in the Scottish Borders with a mate, we took five days and stayed in YHA along the way, great frun, my mum was planning a holiday in Scotland, so she drove us back, but a train back is possible. I was pretty fit then, I was riding time trials and school boy circuit races. We also used to ride down to the New Forest each summer and camp there for a week, that was good.
If you plan to tour and stay in Youth Hostels each night there are loads of choices from Melksham;
South West, acroos the Somerset Levels into Devon.
South, into Dorset, down to the coast, return abit further east to Malborough, home across the downs.
North into the Cotswolds.
West into Wales, head up Chepstow, Crickhowell way, if you're feeling fit, return via Gloucester, forest of dean.
Or as others have mentioned, get a train somewhere and spend a week in a totally new place, a few thoughts, Scottish Borders, Yorkshire Dales, Cheviot Hills and around Kielder Water Area.
If you have any ideas of where you want to go many on here would happily help with route plans, just shout, I would recommend getting the OS 1:50000 maps on soft copy, not that expensive, but at 14, you probably know better than me how to find them for free, not that I would suggest such a thing.