I am planning to visit Grand Canyon during the last week of January, but have only a day to spend there. Any advice on how I can maximize my visit. Also, how is the weather during the time?
Having recently hiked rim to river and back, I can tell you that hiking in the Canyon has been one of the most transformative events of my life. It's beauty is beyond words.
The most important thing to remember is don't be this guy. Take your time, and enjoy the beauty.
Note: I'm assuming you are at the South Rim, since the North Rim is closed. The North Rim is nice, but there is a reason that 90% of the visitors are on the South Rim. The North Rim will be covered in snow, so you can't go there anyway. In the winter its going to be very, very cold at the rim (near freezing), but the temperature will rise about 40 degrees as you make your way down to the river. This has the advantage, however, of allowing you to hike the entire day. From May 1 to September, I was advised not to hike between 10am - 3pm. They were right!
All in all, the Grand Canyon is amazing. If it were me, I could stay a week. At a minimum, you really need 2 days. But if its a choice between skipping it altogether and doing one day, have fun looking over the rim!
I would say it's probably pretty cold, expect snow (it's high there). Taking a look at the weather channel, I can see the temperature these days is in the 40s (0-10°C) during the day. Maybe the mist can be more of a problem, you can check the day before if you are flexible on your dates. Also check the road conditions (there are currently alerts on the National Park website).
And what else than hiking do you expect to do there? You should plan a half-day or full-day trip, no more. From what I remember the multiple sightseeing points offer different angles on the Canyon, so if you spend little time you will still be able to see the Canyon. At this time of year, many paths will be closed (they are announced on the website). So anyway, it's not sure there will be lots to do.
Also figure how far your hotel will be, since the Grand Canyon is in a quite remote area. It can take several hours from your hotel to the rim.
Given I've heard of snow on the ground there in April, it could be very cold.
However, I'll describe what we did, and you can adapt it based on the conditions when you arrive.
First thing was to enter the park (driving) before sunrise. This gave us a chance to park, get our gear together, and race down to Mather Point for a spectacular view of sunrise. Even if it's raining (As it partially was for us) it is still worth it. Mather point is about a 5 minute run from the car park. Give yourself time to get there to be at the front - you don't want a bus load of tourists obscuring your view. Also it's not just about the moment the sun appears, but about the next 20 minutes or so as shadows move around the canyon.
Next, there's the rim route. This is a connection of a few bus routes, included in your pass. Either is good, but we headed west first. The buses are every 15 minutes and stop to drop people off at several points. This was perfect - gave you time to get out, read the info about that point, take some photos, enjoy the view, and catch the next bus.
At the end, we took the bus back to the top of the Bright Angel trail - the most famous in the park. It's steep but manageable - don't try to reach the river though. It was very hot when we went, so we walked down to the first hut - taking just under two hours (lots of photo stops) and power-walked back up in an hour with only one or two stops.
Then we went east along those lookouts - to the end, and then walked back to the camp, in time to catch the west bus once more to one of the two lookouts for sunset.
Now that was in August, and the days were longer. You may find you need to compress your schedule in winter.
Also be aware of crowds - they'll affect the bus queues.
As for weather, their website has updates you can keep an eye on. For example, their latest one:
Average climate, temperature and conditions can be seen on this site.