A day at Dubai International Airport and the city?

As jpatokal said, Dubai is a bit of a sprawling mess, and not much of a walkable city. Depending on your budget, you'd be best served taking cabs from place to place, especially if you're only there for a day.

Having spent a day or two there myself in 2010, I'd say the following were highlights:

• Visit the souk, especially the gold portion to see all the shiny jewelry on display.
• Take a ride on the public transit system. the stations are shiny and new with a futuristic feel to them, taking riders right past some of the most fantastic modern architecture going up in the city. you will see new construction of skyscrapers EVERYWHERE, with the Burj Khalifa obviously being the most impressive.
• If you want to see the city at its most decadent, take the train to the Dubai Mall or the Mall of the Emirates, where you can go skiing or snowboarding indoors among other things.
• Check out the "sailboat hotel" (Burj Al Arab) on the beach. I've heard it has one of the most lavish interiors of any building in the world - they have a restaurant/cafe, but I didn't go in because the prices were commensurate with the decor.
• Go to the beach. Have a swim near the Burj Al Arab, and spot women on the beach there covered head-to-toe in burkas. (Edit: I recommend the Jumeirah Beach Park, which isn't so much "near" Burj Al Arab as "within sight of". It's a public beach, and much plainer than the ritzier, more developed beaches closer and south of Burj Al Arab. It's not as nice as other beaches, but you'll see more local people about and get a better feel for day-to-day life in Dubai. If it's the posh side you're looking for, look for beaches closer to and south of Burj Al Arab.)

In general, the tip to take the metro from the airport into town is a good idea, except when it is Friday. Being a Muslim country, Friday is a special day in the UAE and the metro only starts running at 1 pm on Fridays.

Of course, I got to Dubai on a Friday, but there should be buses, right? Yes, there are a bunch of them stopping in front of Terminal One. The problem is that you can't pay the driver but have to buy a ticket from the machine. With the metro station closed there is only one ticket machine at the whole huge airport. The ticket I wanted was the day pass and it was 16 dirham. Not only did the machine not give any change, it did not accept 'too' much money so I couldn't pay with two tens. I got some change, a tenner, a fiver plus one coin. Well, the coin slot did not work, so I couldn't get a ticket whatever I tried.

My original idea to walk into town did not seem like a good idea, it wasn't that hot but it was quite far and there were mostly freeways around the airport.

In the end, I met a friendly fellow who gave me a spare re-loadable ticket and helps me charge it with 15 dirhams. 14 is actually enough for unlimited rides during one day. It deducts fares for the first few rides and then stops at 1 dirham, all further rides are free.

To answer my other two questions: I could check my luggage all the way through to India with Emirates because I spent less than 24 hours in Dubai. But, yes there are left luggage facilities in Terminal 3.

I could have spent more time than just one day in Dubai, there are enough things to see and the climate is actually nice in February with a nice breeze.

It will be hot during the middle of the day.

Here is what I would do:-

• Catch an early sight-seeing bus around the city (airconditioned and with commentary). You can get off at stops around the city if you see something especially interesting.
• Then go to Wild Wadi. You can put your backpack in a locker there, and have a shower after the rides before returning to the airport.

So long as you take some protection from the sun, it will be cool and a good way to break-up a couple of flights.