When do you eventually get to enter downtown New Vegas?

(At what level do you gain access to the main part of New Vegas,where the Lucky 38 casino is?)

There's no minimum level you just need to have 2,000 caps on your person to get in for free, and they only check you the first time then you can come and go freely. You can also optionally buy a fake passport from Ralph in Freeside for 500 caps that will let you in.

It takes a while to get to New Vegas from Goodsprings though so you're typically going to be somewhere between level 6 and 10 when you arrive, but that really depends on how many side quests you do along the way, and anyway your level is not important.