Hi wab6,
I transit in and out of DXB all the time, and lately I've been staying at the JW Marriott Marquis (taking advantage of the Gold status from UA's RewardsPlus program with Marriott). I've only stayed at about 10 different types of Marriott-chain hotels in the world, but the DXB JW Marriott Marquis has really impressed me with its service. The upgrade to executive rooms are really spacious and quite good, and the executive lounge has a nice free breakfast and dinner (and happy hour) but only from 1830 to 2000 hrs.
On three occasions, I've called and asked for late checkout due to overnight flight departures, and each late checkout has been between 1500-1800 hrs, which is quite generous in my opinion. I've also been allowed to access the free dinner/happy hour after checkout on each occasion, as well as wi-fi. On my most recent visit (5 Jan 15), I was offered access to showers before my hotel departure at midnight (despite checking out at 1800) and the concierge had arranged for lost baggage transfer (UA lost my bags) and rebooking a flight to KBL.
lukedxb is correct that it's the world's tallest hotel. The executive lounge on the 37th floor has a great view, as well as the restaurants/bars/clubs on the 68th (i think) floor. The outdoor seating at the restaurants on the 5th floor (Japanese and Eastern Mediterranean/ME) also have a great view, as you're sitting next to the skyscrapers.
The hotel is in Business Bay, near the Dubai Mall and Burj Khalifa. From the airport, it's about 50-75 AED, depending on the direction (I think the taxis start at 25 AED at the airport, no matter what destination). But in a taxi, it rarely takes more than 20-30 minutes to get anywhere in the city.
There's not much to do in Dubai, so I wouldn't worry. If you check out the Burj Khalifa, make sure to register a time spot online, which will help guarantee a spot during high season, and you'll save almost $100 (I think it's $20-30 online, and $100 more if you just show up, but I haven't been in a few years). With the devaluing of the Ruble, I imagine there will be far fewer Russians during this year's shopping festivals, so the malls won't be as crowded.