Places like the Fox Den are pretty safe - the girls provide CBJ (covered blowjobs) for the most part, and of course condoms are used for full service (vaginal intercourse) and Greek (anal intercourse).
When you look at places like Asian micros (which almost no one would recommend for a first timer), it gets a little more iffy. SOME (and I stress SOME, not all) don't have the best hygeine standards for their sheets and towels, from what I've seen from reviews here. On average, the providers there also have more partners, which of course raises their chance of an STD (and that goes for anyone, not just escorts). However, they can be great bang for your buck.
When it comes to "safety", this really just depends on the provider. Some will not allow digits (fingering), DATY (cunilingus), BBBJ (blowjobs without condoms), or even kissing. When it comes to making a choice, you need to think about what you're comfortable with.
As a whole, escorts are safer than the average girl you'd pick up at a bar. This is our livelyhood so we make damn sure to protect anything that could end it.
The biggest piece of advice I can give you is to research, and shop around. Check out massage parlours, agencies, independents. Read the websites, learn the acronyms, and sit down and think about what you really want, and what you're at ease doing.
Hope this helps