I am thinking of going with 15X10 or 15X12 Rims either 4.5" or 5" back spacing, with a 31X10 L50 R15 Mickey Thompson Baja Claw Radials. I have a 1997 2Dr Blazer with the Sport Touring Suspension. Will these fit without out rubbing?
Sorry, I'm tired and to lazy to search right now.

Picture of my Blazer:

 

for one those rims are too wide for a 10.50 tire, a 15 x 8 would be better, and no they won't fit without lifting. Most use a t-bar crank and shackles, cheap and easy.

 

No... not at all. On factory rims, 31x10.50x15's will fit with a 2 inch body lift. And even then you will rub the frame and possibly the sway bar when turned to the lock. And the factory wheels have 6 inch backspace. If you went down to 5 or even 4.5 inches, you will rub pretty good with 31's. Because your wheels would sit outside the fenders a inch, 1.5 inches.

For 31's and 4.5 inch backspace 15x7 wheels, you'd need a 2 inch body lift, shackles and tbar tweak. And even then you would still have to remove your mudflaps, trim the bottom of the front bumper and possibly cut the back of the front fender some. But after all of that it would look pretty bitchin'! And just so you know the bolt pattern is 5x4.75, or 5x120.67mm.

 

This is probably a dumb questions but how many turns of the tbar do you need to lift it two inches?

Never mind I read the Tutorial.

Ok, for the rims I want as notated in the original post, what size tires would be the best?

 

You can run 31x10.50x15's on 15x10 rims. There is a member here by the name of "bandidolenny" that runs this combo with 5.5 inch backspacing, and 31 inch BFG AT's. If you search for that name and go to his photo gallery you will see what this combo is like.

But he has a 2 inch body lift, a 2 inch suspension lift, trimmed the fenders and the fender flares AND added wider flares to cover the tread of the tire. Some state's won't allow tires to not be covered by at least a flare, normally refered to as exposed tread. Just something to keep in mind and check on to see if it's required for inspection or agianst any laws.

But as I said he has 4 inches of total lift and still had to cut the front and back of his fenders. Here is some link to his photo gallery.
https://blazerforum.com/forum/members/bandidolenny-13624-albums-1998-blazer-z85-10/

 

Thinking about a 29X10.50R LT15 on a 15X8 rim. There shouldn't be any rubbing with this tire and rim combo correct?

 

I had 29x10.50 15 thornbirds on my Jimmy on 15x8 rockcrawlers and at stock height they rubbed. The tires were as big as my friends 31 10.50 bf all terrains. I cranked the t bars a little, trimmed the back of the front fender a little and used flares. I will try to post a pic later, well it will be a pic of a pic, I didn't have a digital camera back then.