There are lots of great locations in Paris, so it comes down to what’s most important to you. I liked staying at Mercure Monty Opera in the 9th, but very close to the 2nd, in February. Unless you are going at the time of a huge fair or convention, your budget is plenty for Paris. Try these sites:
http://www.accorhotels.com
http://www.bestwestern.com
http://www.flyhotel.com
http://www.fastbooking.com
http://www.laterooms.com
 
For Amsterdam, we really liked the location of the Best Western Eden. We had a very cheap rate under your budget, but you have to book well in advance to get it. But try www.bestwestern.com to see what you can get. A few well-reviewed budget hotels that I’ve heard of, for which I really like the locations, are Hotel Brouwer, Hotel Prinsenhof, and Hotel Asterisk.
 
 

Traveler has posted some great site for you.
In Paris, there really aren’t any dangerous areas (except possibly way out in the suburbs), but there are some seedy areas, such as Pigalle.
When you search for hotels, try to do your search with a map handy, and a metro map. Most hotels will be fairly close to a metro station, and the trick is to find one that isn’t too far out of the center, because otherwise you’ll spend a lot of your valuable time commuting on the metro. I’d say to look in Arr 1-12, since higher numbers will be farther from the center.
If you look on the accor site, you’ll likely find lower prices on the weekends at many hotels because on weekdays there are more business people staying at those hotels. Youll also see “hot deals” which are often very good prices— if you’re willing to pay at the time that you book.

amsterdam is a pretty small city, i don’t think it matters where you stay.  the Best Western looks like a good deal
check out eurocheapo.com for hotels