I have found that the burgers at Nathan's are similar to In-N-Out. Obviously not the same, and a bit more expensive, but if you can't get to In-N-Out, it's a substitute.
There are stops for the 119 bus, northbound, (1) on Koval just north of Flamingo, and (2) on Sands in front of Neiman Marcus at the Fashion Show. That bus, the 119 north, will take you to the In-N-Out at Palace Station. Just ask the driver for the Palace Station stop.
Rather than wait for the 119 south for your return, pjs has suggested you could then walk over to Palace Station and ride their shuttle back to the strip. PS often has decent enticements for new players club card enrollees.