There are a number of great neighborhoods with condos in Palm Springs. Regarding location, things to consider are, what do you want to be close to? If you want to walk to downtown, you need to stick to central Palm Springs. If you're into hiking, nature, walking, and quiet, check out the South Palm Canyon areas. Golf? Well, there are five golf courses in Palm Springs alone that are close by to almost any neighborhood in town. The next thing to consider, is the style of condo you want, whether its newer construction, two story or single level, etc. There are some great complexes that are built in the 70s and 80s that have very low density and park like grounds. Some of the newer complexes, are a little closer together, as the price of land has gone up over the years.
There's fee land and lease land too; depending on the area you want to be in, you may only have the choice to be on lease land.....which is foreign to some, but actually once you have a better understanding how that works and what to look for, you can feel confident buying leased properties, which historically appreciates at the same rate as fee (non-lease) land. Some of the best neighborhoods in town are on leased land, so I'd advise you not to rule it out.
As far as safetly, there are very few neighborhoods that aren't safe...in fact, I can't really think of any in the Palm Springs area.
I have been selling condos in Palm Springs for almost 10 years and know just about every complex in town. I'm happy to answer any additional questions you may have. Feel free to visit my website page that is dedicated to condos: http://www.paulkaplanrealtor.com/CondoConnection.php
ALSO....unless you are paying cash, I'd strongly encourage you to talk to a lender first to understand the various programs available for foreign nationals. I have more information on this topic at http://www.paulkaplanrealtor.com/ForeignBuyers.php
Happy to help if you have any questions! Its a great time to buy, as there is a lot of inventory and smart sellers are much more negotiable then they've been in the past few years.