Short answer, stick to the Dunes, and especially the Mountain course at the La Quinta Resort. Stay somewhere else though.
Here is the long, detailed answer. Fortunately or unfortunately I know a good bit about golf in this area. I tried to cover a lot in my response, but if I missed anything just shoot me a message and I'll try to get back to you soon....First, you should be aware that there are reports out there that both the La Quinta Resort and PGA West have filed for bankruptcy. I don't know how true this is or any details behind it. I do know this though. I have been to PGA West/La Quinta Resort 4 times since 2007 and I have definitely seen a turn for the worse, especially at the golf courses at PGA West. When we first played PGA West back in 2007, it was really nice with lots of amenities that you would expect. Everything from the driving range to ball markers to tees to bottled water were included in the greens fees. When I played there last year, the driving range was shut down (we couldn't even pay a fee to use it), there were no freebies anymore, and most disturbing to me was that there was no longer bottled water. There were coolers every 5 to 6 holes or so out on the course, but two of the three we ran across were empty. At $235, there should be plenty of water available on the course. After that last experience, I vowed never to return to PGA West. Everyone says you need to play the Stadium course at least once just to say you played it. If you feel that way, then go for it. It's a nice course and so is the Nicklaus course. They are no better than many other options in the area though and they cost a lot more.
In terms of the resort itself, it's not what is used to be. There was a time when this was a great place to stay. That time has ended though. It seems that it has gone downhill since the Hilton took over. I have tried on multiple occassions to bring this to the attention of the Hilton staff, but I have been blown of or ignored each time. I get the impression that they know things are going down hill and they just don't care anymore. If you are looking for a nice resort, you are probably better off at the Hyatt or Renaissance resorts in Indian Wells or the JW Marriott in Palm Desert. The Hyatt would probably add 10 minutes to your drive to the golf courses, but that's not so bad if you ask me. Plus, it's not like staying at the La Quinta Resort gives you any discounts on golf.
I know this has kind of been negative thus far. There is some good in here though. La Quinta is one of my most favorite places to play in the US. The two courses at La Quinta Resort (Dunes course and Mountain course) are both solid options. The facilities are very nice and there is a beautiful driving range that has a huge mountain as a backdrop. The only down side is that you can only hit irons here, as the base of the mountain and the hole the hugs it would be within reach if hitting a driver. The staff here is great and they keep things moving. Pace of play was never a problem on either course. Both are kept in very good shape. The Mountain course easily has some of the coolest holes I have ever played. About half the holes hug the base of the mountain. Two of them are in a box canyon and the par 3 16th has a huge elevated tee and is one of the coolest holes I have ever played. If you could only play one round, I would make it at the Mountain course at La Quinta. The Dunes course doesn't have nearly as much hype as the other courses, but it is easily just as nice as the courses at PGA West and cheaper too. 6 of the 18 holes are on the same side of the property as the Mountain course and have great views. The other 12 holes are more of your typical resort course with houses lining the fairways. It has a nice, fun layout though and is worth playing once. The Mountain course is definitely worth a return visit though.
Here is a tip to save some money. If you can handle playing 36 holes in a day, you can play one course in the morning for the regular rate and then play a different course in the afternoon for a fraction of the price.
I also want to point out that the La Quinta Resort is actually a 5 minute drive from the golf courses. Not a huge deal, but people should be aware that the courses are not "on-site".
Lastly, if you have the time, check out the course at SilverRock. It is also just a few minutes from the La Quinta Resort. It is a great course, but it's owned by the City of La Quinta, so they keep the rates very affordable. If you are playing in September though, it should be pretty cheap everywhere. Most courses in that area don't raise the rates until October.
I tried to cover everything, but let me know if there is any other info I can provide you.