My son has this Dawes Espoir 3000 26" :
http://www.bikes2udirect.com/B3196.html
Its pretty good because its light and has sufficient gears. However, I fitted Marthon tyres to it for the trip. Some short parts of the route are quite rough and I was glad I did. The route from Holy Island to Berwick at one point was across a field and the last part through the Tweedale valley route to Innerleithen was along some very rough stoney tracks. This wasn't for very long though and to be safe we pushed the bikes on the worst bits which were very short. The vast majority of the route is on tarmac or very good cycle tracks. Mine is a Dawes Galaxy Ultra.
We also paid £60-80 per night for a twin room including breakfast, except Edinburgh where we stayed in a Holiday Inn Express during the Festival when the prices jumped up to £150 per night. A lot of the B&Bs only take cash or cheque (no credit cards) and some you have to pay all or part in advance by cheque.
B&Bs we stayed at were:
York House Hotel - Whitely Bay - Large room, good breakfast - 0191 252 8313
Togston Hall Farmhouse - nr Amble - Very friendly & helpful, quite location - 01665 712699/07894 035 738
The FarmhouseGuest House - Belford - Very friendly, very comfortable - 01668 213083
Alannah House - Berwick - Very friendly, great breakfast. Noisy seagulls! - 01289-307252
The Old Priory - Kelso - Friendly, good breakfast, rooms at the front noisy due to cars on the cobbled street, bikes kept outsise at night - 01573-223030
Glede Knowe Guest House - Innerleithen Very good, great breakfast - 01896 831295
Holiday Inn Express - Edinburgh - Busy typical Holiday Inn, room very hot, bikes stored in locked store room 0871 423 4876
Blyth was okay to navigate (although some of the blue route 1 signs are confusing and in places wrong) because I planned the route and used a GPS app on the iPhone. However, its an urban area away from the coast and compared to virtually all the rest of the C&C is not very enjoyable.
As carolonabike says the Moorfoot Hills on the last day are not too difficult. However, with a youngster it is a bit different and my son did get a bit fed up with the constant climb and I just had to make sure we stopped a bit more often. However, he loved the run down the other side!
Take care in the cente of Edinburgh. Although there are cycles lanes on nearly all the streets, it was very busy and there were tourists walking along the cycle lanes. September should be quieter though.
In Edinburgh I'd highly recommend taking your daughter to the Obscura (my son loved it):
http://www.camera-obscura.co.uk/
If you're going to be using a GPS and want me to send the gpx files for the route just let me know. I'll just need a couple of days to tidy them up for the parts where I made an error or took the wrong turn!