Hi Pam,

to the forums! 10 days is a decent amount of time to see at least a couple of destinations in Thailand. You will likely be arriving and leaving from the capital Bangkok, so I would suggest topping and tailing your stay in Bangkok with maybe a couple of nights each "end" of your holiday. There is plenty to see and do in Bangkok - the Grand Palace, (floating) markets, the nightlife, amazing restaurants, organised tours/trips, cooking classes and more - so a couple of "doers" like yourself should be able to get out and about and see lots of things!
Any reason on why you chose Phuket as your other destination? I would place it as more resort-oriented than sight-oriented, although of course it does have shops, beaches, activities like snorkelling trips, diving trips, jetskis and so on. Somewhere like Chiang Mai in the north is much more of a "doer" destination, where there is plenty of cultural/historical sights, activity trips like elephant trekking through the jungle, visiting old temples, going rafting etc. Something to consider though is that virtually anywhere you go on Thailand in October it will be wet season, so expect more rain than usual.
Your mileage may vary, but I would also consider a third destination close to Bangkok for a bit more variety. Kanchanaburi is only a few hours away by bus and has the Bridge on the River Kwai, Hellfire Pass, the War Cemetery and a couple of War Museums, as well as Erawan waterfall. It's very "sight-heavy" and also a lovely, relaxing rural destination so I would definitely put it on your list.
So maybe something like
Day 1. Arrive BKK - a nice meal, recover, relax
Day 2. Out and about in BKK - see Grand Palace and other sights, markets, shopping, eating, drinking
Day 3. Get early bus to Kanchanaburi, see Bridge on River Kwai, Hellfire Pass, cemetery, war museum, erawan waterfall, other sights. Stay overnight in Kanchanaburi
Day 4. Back to BKK to fly out to Phuket. Settle into Phuket
Days 5-8. Phuket
(lots of locations - people can advise which is best)
Day 9. Back to Bangkok, more sights, final shopping
Day 10. Fly back home!
Just an idea!
HTH
Steve