While you are in the process of hand-training, make sure your hamster plays/explores in a confined area, such as a bathtub, pet playpen, or a kiddie pool. Whatever he is in, make sure the sides are higher than his climbing ability. Walmart carries a "pet playpen" for under $10.00, and I have used several of them (you can buy several and hook them together for a large play area) -- and have had several escapes! If you use a pet playpen, make sure you stay with your hamster at all times- they always seem to wait until you are not looking to climb out!
If your hamster has finished hand-training, whatever areas/room(s) you have hamster-proofed will be his playground. Be sure to remember the safety guidelines before letting your hamster freely roam any room.
Change up your hamster's playground DAILY. If you are still HT, a change in location is also good. (Today the bathtub, tomorrow the kiddie pool.) Make sure the toys/objects you use are not placed close enough to the sides of the enclosure that your hamster can use them as a ladder to climb out.
Toilet paper/paper towel rolls, wadded up paper balls, twigs/sticks, small boxes, different sizes/types of wheels, plastic bowls, old shoes, mazes, tunnels, sand bath
Let your hamster climb all over you in the tub (great for bonding) Hide food/special treats in a box/bin and have your hamster find them, Hide treats in the bottom of a bin full of bedding/sand and have your hamster dig them out, Put your hamster in your shirt pocket- see how long he will stay there, put your hamster in a "roll-around" ball for 20 minutes Hamsters LOVE laundry! The bigger the pile, the better. (They will also rummage for hidden food and treats inside.) Build a hand-crafted maze for your hamster out of cardboard or anything safe.
If your hamster is hand-trained, hide special treats all over the room for him to dig out.