You're not going to have the same kind of problem with flea pits in Spain that you would in London. Also, public transport in both Madrid and Barcelona is cheap.

Download a map of the Madrid metro and print it out - use it as a reference when looking for places to stay in Madrid. Just discard anything that is too far out of the way. My own friends live in the Sol/Atocha area which is a great area if you want to go for tapas in the evening and clubbing at night. Even so, El Prado and Reina Sofia museums are easy enough to get to. To be honest, most places are - the metro system is efficient and cheap.

My concern about your enjoyment of Madrid is that apart from museums and galleries, you've not really commented on many other interests. And most of the museums and attractions in the city are things you have to pay for.

I thought you might enjoy Barcelona more because it's a city that seems on initial visits to have more hidden treasures (Madrid does too but you might find they are TOO hidden, or not to your taste... I find the citiy's best delights are more 'social') just walking around the Ramblas, Montjuic, El Barrio Gotico, Gracia, Parc Guell, the Port area, etc, etc... will be fulfilling, easy to do and for the most part, free. And there is a more of a 'left field' leaning in Barcelona, not something I can explain easily - if you knew the difference in programming between Tele Madrid and TV3 (The main Catalan channel) you'd realise quickly that Barcelona is more supportive of contemporary Art than Madrid is. It means that although there are plenty of fine museums that require payment for entry in Barcelona, you're more likely to stumble across small galleries and spaces with installations that won't charge admission.

As Kaptan says, look for Hostales or Pensiones. you'd have to be EXTREMELY unlucky to come across one that was unhygienic... I've certainly never come across one, nor heard any horror stories.

The main problem in Spain is theft and the occasional run in with con artists (some of whom pretend to be policemen in order to get your wallet and documents). Take the same kind of precautions as you would in New York - don't just sling a bag over a shoulder so that it can be cut or snatched away easily - something I myself have seen happen far too many times in the Barrio Gotico. Nevertheless, I've never had a problem. If you're both sensible and take precautions, I doubt you'll have a problem either. Just be sure to be wary of leaving anything valuable in your pension or hostal room.