Radio Tower Overlook via Hayden Trailhead is a 3 mile round-trip hike is only 20 minutes from downtown Denver and offers a view of the city from this overlook.
I loved this trail when I lived in Lakewood. It has a decent elevation gain, close to the city, spectacular views, and you can pretty much hike it year round unless you just had a winter snow storm (though you could just hike in snow boots!).
Take the John O Hayden Trail from the Utah Parking lot along Alameda Parkway. You continue up this trail until it intersects with the Green Mountain Trail and you head East towards the Radio Tower. You really can't miss it, as it's a plateau, just walk towards the radio tower! You can walk out on to the overlook for a great view of Denver as well.
It takes about 1.5 miles to reach the radio tower and when done hanging out and taking pictures, simply return the way you came. This is a great 1-2 hour hike if you're in the area!