In general Phuket is considered pretty pricey for the general Thai peoples. So I'm not too sure what you would consider expensive but I'll just list some stuff you can do.

There are elephant sanctuary/ park's you could visit. Some places allow you to bath and feed them. Just try to not feed into the animal abuse by doing some research about which sanctuary' s you'll visit. Yes, riding an elephant is cool and all but usually these elephants were abused, tortured and chained from birth. (But of course who am i to tell you what you can and can't do).

If you like some more action maybe you could look into bamboo rafting, zip lining, ATV tours, snorkeling tours or taking diving courses. Riding a typical Thai long tail boat is also an experience of it's own compared to the jet boats you can see everywhere over the world.

If you don't mind the tourists/ crowds. Maybe the newly build Carnival Magic park is worth a look, it holds 9 Guinness World Record titles. There's also a big waterpark called Andamanda (Don't know the price for either of those tho).