Re Richard L. posting that: "As another poster has noted Jackson, Wyoming is the closest airport, and in the summer there are many flights in and out of there."
An alternative to flying into Jackson is to fly into Salt Lake City and take the following shuttle from SLC airport to Jackson:
http://www.mountainstatesexpress.com/jackson_saltlakecity.html
Prices and schedule provided at the above site indicate the shuttle takes about 5 hours each way and costs $70/person each way.
Haven't used this shuttle before. We might check it out in a future trip to see if overall cost of flying into SLC and taking the shuttle from SLC to Jackson would be significantly less than flying directly (expensively) to Jackson.
And re Richard L. posting: "Jackson also has enough guides, outfitters, people looking to make a few dollars, etc so that you could arrange for transportation to/from the hiking venue."
We used one of those Jackson taxi services (think it was called Stage Coach Taxi) to get from Jenny Lake campground to the trail head (Teton Village Tram!) for our hike along Teton Crest Trail a few years ago. We only needed a ride at the start of the trail because our hike along the Crest Trail brought us back to Jenny Lake.
That one-way taxi for two persons totalled about $35, which we believed was a great deal for the convenience of scheduling when/where we wanted to go.
Finally, re Richard L. posting: "Note that campsites must be reserved in the Park, which sometimes can be done online:
"https://backcountry.grandtetonpark.org/""
Unless changed since last year, backcountry camping permits required in GTNP are available on-line — but there's a cut-off date for reservations on-line. I think the cut-off date is sometime in May (maybe even earlier), so check the website.
A few things to note about the need for GTNP backcountry reservations (and which may apply for other National Parks, too).
First, if advanced reservation aren't made, there will still be a number of permits kept available for folks to obtain at the park the day before starting a hike, but those can run out quick depending on time of year and trail (August – bad generally; late September – a whole lot better; Teton Crest – popular, but we had no problem getting last-minute permits for the Crest Trail per the following).
Second, backcountry permits are for camping in designated zones, with permits often only for specific campsites in a zone.
It may be possible to obtain a permit to camp in a "camping zone" at the last minute — even if all of the permits for specific "campsites" in the zone have been taken already. But that's an option that varies in availability depending on which ranger you're talking to at the desk, and probably with the route desired, too.