Well, that depends a lot on what you're looking for really and how much money you want to spend.
I find Leeds to be a fairly vibrant city with a good balance of employment, shopping and entertainment. It's not struggling in the recession quite so much as it's neighbour, Bradford. It's perceived as a little more 'high class' than Sheffield or Manchester, but not as 'snobbish' as York or Harrogate. (And without the prices of the last two!)
I'm in West Leeds myself, Bramley area, so that's where most of my knowledge is based. I did some research on Pudsey too before I moved, so can mention there too. Hopefully someone else will wander along in due course to talk about the other areas of Leeds!
Where I'm based, transport connections are pretty good, I find. There are both train and bus stations in New Pudsey and Bramley which makes getting into either Leeds or Bradford relatively easy. From Leeds there's easy connection to York/Sheffield as well as the London train. From Bradford there's easy connection to Manchester.
Leeds/Bradford airport is relatively small, but seems to operate pretty smoothly on the whole and works ok for flights, though not much/any long haul is available. I've never noticed a problem with noise from planes overhead, I barely even notice them half of the time! It's apparently more noticable in Rawdon. For longer flights, the huge Manchester airport is about an hour away by car or relatively easily reached via train - as long as you don't attempt it in rush hour!
Shopping is also pretty good. Leeds city centre is pretty much what you'd expect with at least one of most big chains and a splattering of smaller shops. For local shopping, Pudsey has a proper town centre with pretty much everything you'd need, and has an absolutely massive Asda and M&S nearby at the Owlcotes centre.
Bramley has a smaller shopping centre with a reasonable little Tesco there. It also still maintains a post office. Couple of nice little extras too like a butcher, baker and a couple of pharmacies. There are two reasonable sized Morrisons within easy reach, one of which is at a small retail park down in Kirkstall.
For public services, I've not had any experience with the schools so can't comment there, sorry! Libraries are dotted about all over the place and all connected to the bigger Leeds system - so you can get books at one and return to another. They can source books from one another too. There are Libaries in both Bramley and Pudsey.
Leisure centres are pretty good. I've not been into the Pudsey one, but nearby Kirkstall has a large modern centre that does most activities. Bramley Baths is a revamped historical baths that has a lovely quaint feel to it and great for a swim, though lacks amenities for other sports.
My local doctors surgery isn't too bad, though getting an appointment outside of working hours is tricky. However there is a walk in NHS clinic in the middle of Leeds that can be quite handy, if impersonal. For dentists, there are a few NHS ones around and I managed to register ok, but people recently have commented having a difficult time.
I've visited both Bradford Royal and Leeds Infirmary for hospitals with various people and neither are exactly awe inspiring, but they're modern and servicable, doing what they need to. St. James is apparently a lot more friendly, but a little behind the times on equipment.
Refuge collection is generally pretty good. General waste is collected every week, recycling is every four weeks. During the summer, garden waste is collected every two weeks. Recycling is paper/plastic/tins and all thrown into the same bin. Glass is not currently collected.
Water is provided by Yorkshire Water in the area. I find it tastes pretty good, personally! Never had a problem with discolouration or such, pressure is maintained and it's normally freezing cold. It's slightly on the harder side, but not got too many deposits to clog up appliances.
Houses, in my area at least, are mostly three bedroomed semi-detatched or townhouses. Getting a much larger house might be a bit trickier, and there'll almost certainly be a premium attached. However, getting a flat is likely to be very cheap currently, as Leeds was a bit gung-ho with building flats before the recession and there are quite a few still empty now that they're flogging cheap.
A few comments on other areas that I've heard via the grapevine... Apparently Roundhay is pretty good, and I've heard people say approving things about Morley as well. Armley is where the prison is, so it's whether that would concern you or not.
Calverley and Rodley have a slightly more 'village' feel to them, with a particularly strong community in Calverley. However, they're a little further out so transport links suffer a touch and shopping isn't within walking distance.
Not heard particularly great things about the Beeston area or down near Elland Road, so might be an area to avoid. Unless you're a huge football fan!
Headingley is probably best avoided as it is very much 'studentville' for the University. The town centre consists mostly of off-licences and take-away places. Throughout most of the year there is a near constant throng of costumed students doing the 'Otley Run' between the drinking establishments. However in summer it is pretty much deserted.
Kirkstall isn't too bad, but is situated quite close to Headingley and also has several student residences there.
Horsforth seems to be where the post-grads go to live, which may or may not be an issue. It has a fairly long high-street with reasonable shops from the times I've passed through.
Hope that helps a little. Post up any questions and I'll answer them as best I can! If there's a specific area I've not mentioned, let me know - I'll grill my colleages for the general feel of the place from the locals!
Alternatively, check out the Leeds Government website for more information on various things.