There's an open top bus that goes between Dawlish Warren and Teignmouth every hour. It's the 222 or 221, I cant remember but it's a bit too quick!
Teignmouth is lovely, make sure you walk the back street near the harbour, the ferry across from Shaldon is fun and very friendly. As is the life boat house/museum.
Peabodys do amazing pancakes and reasonable coffee and have sofas in the back. It looks a bit run down but is very child friendly.
Make sure you check out what is on at the Pavillion as they often do workshops for children although they are a bit pricey. TAAG also do children's workshops but usually only in the holidays.
The best seafood in the area is at The Crabshack but you do need to book quite far ahead.
Best ice cream is from Jane's but it might not be open this time of year.
The scooter park and playground near The Den are great. The playground has a splash park which is only working about half the time but worth taking a couple of towels just in case.
The beach at Dawlish Warren is the nicest out of the local ones. It gets crazy busy in the holidays and Teignmouth beach is often quieter. Its also a much longer walk from the car park at Dawlish Warren. There are plenty of arcades if that's your sort of thing.
A really good thing to remember In case it rains is that several of the caravan parks in the area do day passes for their facilities including swimming pools. So if does rain then you can always go there for a swim. Lady's Mile is one and another is Cofton. The lido at Teignmouth is nice but the shallow end is still quite deep and it can be cold!
Let me know if you have any questions I can help with!!