We actually weren't planning to walk to the Sun Gate on our free morning at Machu Picchu. Most trekkers come in through the Sun Gate, as it is the end of the Inca Trail. But for those of us who didn't trek, the Sun Gate is about a mile up from the main site of Machu Picchu.
In August, the sun rises at about 7am, and the line into Machu Picchu was no joke either the afternoon we arrived or the next morning. In order to get to the top of the Sun Gate, we would have had to line up well before 6am in order to hopefully get in the gate as quickly as possible and make it to the Sun Gate. Instead, we decided to hike to one of the upper points of the ruins, and enjoyed the sunrise from there. We were concerned that the Sun Gate would be really crowded, and that we might not make it up to the Sun Gate anyway, because the line just to get in was really long. The view from here was fantastic, and most visitors stay farther below so it wasn't crowded at all. After watching the sunrise, we decided that it would be fun to walk to the Sun Gate anyway, so off we went!
How long it takes you to hike to the Sun Gate depends on two things: how fit you are (and how you handle altitude) as well as how much time you spend on the way up taking pictures of the beautiful view below. Most guides suggest that it will take 1 to 1.5 hours up and about 40 minutes on the way down. It took us about 1.5 hours or a little bit more roundtrip and we spent probably 20 minutes or so at the top. If you have problems with altitude, it will definitely take longer–we passed many people who were having a really hard time walking uphill at 9,000 feet.
The Sun Gate was to be the main entrance for the Incas to Machu Picchu, and does provide a stunning view of the entire site. But as our guides said, if you are looking for the "best view ever" you might be disappointed–Machu Picchu does look really small from there. If you are just interested in getting a fun hike in and some good views, the Sun Gate is absolutely worth it.
That said, I think whether or not you walk to the Sun Gate really depends on how much time you have at the site: if you are there just for a few hours or half-day in the morning, I'm not really sure–that unless you just want a fun hike–that the Sun Gate is worth it. Because we were able to spend the entire afternoon prior exploring the site, until Machu Picchu closed, the next day there wasn't a ton more that we really wanted to see, and the extra bit of exercise definitely sounded nice (marathon training, remember?).
Overall, here is my verdict on the Sun Gate:
Hike: Uphill, but easy path with some stairs.
Length: 45 minutes up if you are fit/not having altitude issues; 1.5 hours if you are having a hard time.
View: Excellent, just to take in the expanse of Machu Picchu and the surrounding areas, but there are lots of fantastic views throughout the site as well. Can be hazy/foggy, and depending on you camera and skills, lighting can be tough. So if you are going up just to get a good photo, you may be disappointed.
Overall: If you have time and want exercise, it's definitely a fun hike. If you are doing it just to say you did (come on, we all know people like that), or for the one and only perfect shot of Machu Picchu, well, you might be disappointed.