I may be wrong...don't have time to look it up...but I think the Kenai is draw permits because it's so close to Anchorage.
You are wrong, you should have looked it up...Some areas are draw, but most everything is OTC or registration minus caribou. The restrictions are more so for NR than residents.
Draw statistics are in the special draw suplement which will come out next month some time. The drawing deadline is the 15th of December this year.
Pull up the regs and read cover to cover. Look at page 35, it details how to read the information for each unit. If you plan to hunt as a NR its your responsibility to know the rules and regulations. AK regs are about the easiest I've ever seen to be honest, once you understand how to read them. The state is broken into 26 units... some units are bigger than most states in the L48. Most of the unit bag limits (8 species) are described in 2-4 pages.
You have 3 different permits.
HT (harvest ticket) is OTC to anyone, free for residents, and costs NR $tag fee
Registration is open to anyone, same applies above for cost, but its limited to a harvest quota.
Draw, limited to number of permits given.
If you want to see maps for special draws get on line and look them up.
The only thing I'd look into hunting on the Kenai is black bears. Everything else is an "extreme" DIY type hunt in some of the wettest/brushiest country north of the panhandle, or ATV hunt with 1000 of your closest freinds.

Lots better places to hunt in AK, but not many better to fish. Can't have both up here.