Las Vegas is at about 2,000 feet in elevation in the desert, so very hot summers match colder than you'd think winters. If you can plan your trip to Vegas around spring or fall, those are probably the best for most outdoors activities. Of course, you could come for the Las Vegas Marathon in early December or for Silverman in November if you wanted to plan around a race.
There are two great places to get out of Vegas, Red Rocks on the west side of the city and Valley of Fire/Lake Mead on the east side of the city. Las Vegas is surrounded by federal land, so once you leave the metropolitan area, it gets wild pretty quick. Either one is pretty easy to get to from the Strip if you have a car, but a big pain if you don't have a car - neither will be a cheap cab ride.
Mount Charleston is another good destination, and can be a little less crowded than the other two - neither of which is off the beaten path. Go in the winter and there is a small ski area, or go in the summer for pleasant hiking in the mountains.
There are five national parks that make for great 3-day weekend destinations from Vegas - Grand Canyon, Great Basin, Zion, Death Valley, and Bryce Canyon. Out of those, Zion National Park has to be the best weekend destination from Las Vegas - less than three hours from the Strip, you can be in one of America's best national parks, where hiking options are limitless.
In the other direction, you can north head from Las Vegas to Great Basin National Park in the summer to hike thirteen thousand foot tall Wheeler Peak.
Mount Charleston is the best place to go for high-altitude hiking - from the Strip, you can be up into forests in an hour, and you can summit Mount Charleston if you have all day for the hike.
Running down the Strip in the morning - you'll see runners do it, it looks like fun, but it's really not. The lights don't really work with you, so you'll have to break stride and use the pedestrian bridges, there's a lot of concrete, and if you wait to long, you'll have to dodge tourists. It's a lot less interesting, but the running on the streets parallel to the strip right behind the big Strip casinos is a lot easier. Do it once and see if you like it.
Red Rocks is a great place, but it can be very, very crowded, especially on weekends with cars and traffic jams.
Spring Mountain Ranch State Park is really underrated - right past Red Rocks, it gets none of the tourist traffic that Red Rocks gets. It's not the same as Red Rocks, there's no scenic drive, epic trails, or rock climbing, but that's part of the charm.