While this is certainly something kids will enjoy, most feel the fun ends within the first 10 minutes.
The truth is that riding an elephant is one of the least interesting things you can do with one.
Alternatively, mahout training, while it certainly won't leave you with any sort of real certification, does entail a significant amount of interaction with the gentle giants including a ride on the elephant's neck, some simple commands, and bath time in the river.
Neither option will offer enough interaction for some, but you will get closer to these animals than most people ever do, plus you're supporting a good cause. Almost every tour company offers some variation on these trips. Spend some time exploring your options for a package to fit your interests and budget.
Prices are noticeably higher than similar experiences in Thailand, but the listed elephant centres are sustainable, humane and provide excellent care.