I assume with kids?
The Donkey sanctuary is nice and some lovely coast path walks nearby...including to the nudist beach so watch out!
Pecorama model railway Centre is good for young kids who like trains...or grown ups who like them too.
Seaton tramway.
World of Country Life in Exmouth for farm animals and soft play type of things.
River Exe cafe (on a boat), Exmouth. You can also get the ferry over to Starcross on the other side of the river and from there you can get the train to Dawlish Warren or on to Dawlish. Dawlish Warren has some fairround rides and go karts as well as the lovely beach and nature reserve. You can walk from Dawlish Warren to Dawlish along the sea wall.
Cycle path from Exmouth to Exeter.
Topsham - can drive, get the train from Exmouth or cycle there. Nice shops, restaurants & pubs. Darts Farm for food and shopping.
Near Exeter, Crealy Theme Park.
Greendale Farm shop hsd some animals outside aimed at younger kids.
Wildwood, used to be called Escot, back up near the A30 is a great country park.
Woodbury common is nice for walks.
Bicton Park is great (but expensive) for young kids.
Lovely walk from Otterton Mill (nice for coffee, lunches and ice cream) along the river to Budleigh Salterton. Lovely pebble beach, good for kite flying. Nice cream teas.
A la Ronde is a sweet little National Trust Property near Exmouth.
If you make it all the way up to Exeter then there's a clip and climb on Exeter Quay. Also kayak hire, bike hire, a bowling alley and lots of restaurants. In the Marsh Barton area just along from the quay there's a climbing hangar for bouldering and a trampoline park called ibounce.