Langjökull Glacier, Iceland's 2nd largest icecap, is more or less a seemingly endless expanse of ice and snow nearly 5,000 ft (at its highest) above sea level. During the warmer months, this brisk arctic wilderness can be accessed from Reykjavik via either the F550 or F35, although you'll be needing a super-jeep/snow mobile year round if you want to get out onto the ice in a hurry. For anyone on a tight schedule, this popular method is your best bet for a single day adventure tour here.
If you've got the time to do some serious exploring on Langjökull, there are available hiking tours and ski crossings that tackle large swaths of this 50 km long/20 km wide glacier, usually running about 2-3 days. Depending on your guide and your curiosity, you can pair these up with a tour of a man-made sequence of underground caves and tunnels built as a tourist attraction; apparently a chapel will be completed at some point so that travelers can get hitched inside the ice. An interesting proposition, although we're guessing it won't outdo Vegas.
A quick word of common sense caution: just because it's the nearest glacier to the Icelandic capital doesn't mean Langjökull is a traveler-friendly destination. Cracks, crevices and moulins present a serious danger on this (and every) icecap, so unless you know the area extremely well we'd highly recommend spending the extra money to go with a guide. Then just remember to pack your warm/waterproof gear and get ready to experience one of Iceland's most formidable glaciers.