Actually, you can't camp out on the range.  It's only open to the public
during daylight hours on those two weekends.  There are two visitation/travel
options:

1.  You can access the site from the north (US highway 60 if I remember
correctly) during the daylight hours.  It's probably about a half-hour drive
in from the highway.

2.  You can caravan in/out with military escort (sort of a wagon train) from
the south end - this is about a 75 mile trip each way.

Of course, you can do both, travelling from north to south or vice versa.

There's a wildlife refuge near the north end - October is often a good time to
catch migrating birds.  I'm sure that there's camping nearby as well.