It depends on the points. I'm generally a point hoarder, myself, and like to use them for big trips when possible. I pay for hotels/flights out of pocket when I can to accumulate more points. Amex Platinum is 5x points on flights, for instance. I flew back to Phoenix in November and transferred Amex points directly to Delta and used them on Delta's site to book.
It's kind of a balancing act for flights. You can book your flights through Amex travel for instance, but you generally get a better redemption value transferring them to whatever airline you're using. When I'm booking flights with points, I try to be as flexible as I can be with dates and use google flights to find the lowest possible fare. I'll then transfer and book directly through the airline.
If you're looking to travel more internationally and really get bang for your buck on points;
https://www.going.com/ is a great site. It'll email cheap flight alerts to all sorts of destinations that are considerably much lower than regular pricing.
You can go deep into this with transferring points to certain airline partnerships and what not.
If I recall you said you were an Amex guy, correct? And I'm guessing you fly AA being at Sky Harbor?
