We live in England and hoping to get some sunshine and pool enjoyment around late April in the USA.
which one of these cities will be warm enough to swim and get some tan?

All 3 will be warm - but if an ocean is important to you rather than pools, obviously you'd have to go with Miami.

My personal favorite is Vegas! There is a lot to do there. I don't gamble but my husband does occasionally and I love it there. Most of the hotels have beautiful pool areas. I have been there 7 times in 4 years and it just keeps getting better and better. During the day you can lay by the pool or drive out a ways by the Hoover Dam or Valley of Fire, the scenary is beautiful. At night down the strip there is a lot of free things to see such as a volcano erupting, pirate ship sink, water ballet, the eiffel tower, a pyramid. I could go on and on. So if you wanted a vacation full of sun(&pools), great things to see, excellent shows this would be the place to go! If you have any questions e-mail me.

If you like waves, sun, palm trees, margaritas and cruise ships go to Miami.

Miami isn't for everyone. Alot of people find the crime issue to be too much and ruin the enjoyment of their vacation.

Phoenix has warm weather, but that's about all that it has to offer. Sedona is a beautiful nearby area for a day or two, but not known for it's swimming.

Las Vegas would be my choice of the three. Lots of resort style pools to choose from and lots of nightlife and good restaurants.

I agree with the above posts - All 3 will be warm enough for a swim/tan. I would also pick Las Vegas because there is a lot to do in a compact area. Plus there are some good day trips you can take from Vegas. I live in South FL, so I can't recommend it....but we have gobs of tourists year around. I have been to Phoenix several times (friends live there) but would not consider it a tourist destination. Go to Veags, you'll have a blast!

miami if you want the ocean.
otherwise, vegas. pheonix will have great weather but unless you golf, it's pretty boring. you don't say how long you will be there. i find 4-5 days in vegas is PLENTY so if you are planning a longer vacation, maybe consider making another stop (palm springs?) p.s. hotel rooms in vegas are much cheaper mid week.