The easiest and most accessable herd would probably be the Mulchatna herd out of Dillingham.
You might look at doing a float trip on the Mulchatna river. This would allow you to possibly stalk a caribou along the river rather than out on the open tundra.
You need to remember that you cannot hunt in Alaska on any day you have been in an airplane. This makes being dropped off for the day impossible. Since caribou roam over areas larger than most states aircraft are the preferred method of travel.
The last time I priced out a Beaver on floats it was about $800.00 an hr. and that was a number of years ago. When you figure that you are paying for airtime both ways on each trip it can get pretty expensive pretty fast.
A float will let you cover alot of ground, access Bear and Moose, enjoy some great fishing and allow you to have more gear.