That depends on where you want to travel and if you already have a permit from your own state.
FL and UT are the two most recognized out of state permits. Both of their non-resident permits will let you carry in 29 states, the coverage is almost identical. Not all states that have reciprocity with FL and UT honor non-resident permits though. I have removed those states so according to the list from handgunlaw.us:
Both FL and UT get you:
AL,AR,AZ,DE,GA,ID,IN,KY,LA,MO,MS,MT,NC,ND,NM,OH,OK,PA,SD,TN,TX,UT,VA,WV,WY
FL adds:
FL,KS
UT adds
MN,WA
As more states gain reciprocity with each other the value of the UT and FL non-resident permits is diminishing. When I got my UT non-resident permit in 2005 KS, where I live, had no CCW permit at all. Now we have a pretty good shall issue permit and reciprocity with 20 states. 16 of those overlap with UT but I get CO,MI,NV,KS, and SC added.