In a 15 day Texas trip, how many days in each city: Dallas, Austin, San Antonio, Houston?
It really depends on what kinds of things you like and if you are traveling with kids. I have lived in Austin and San Antonio and spent a good deal of time in Houston and have been to Dallas several times.
I would spend 3-4 days in San Antonio, depending on if you want to add things like Sea World or Six Flags. You can go to the river walk and the Alamo and the central Mexican Market there and maybe see some traditional dance performances.
I would probably do either Dallas or Houston but not both. They are sprawling cities with a lot of traffic and chain stores and there are more distinct things in other parts of Texas. I would probably choose Houston and go to Nasa and the museums. Houston is extremely diverse and has very good ethnic food. 2-3 days there would probably be sufficient.
I would spend the rest of my time in Austin and Hill Country.
Hill Country is between Austin and San Antonio, and it is one of the best parts of Texas. You can do wine tasting, tube down the river, visit Texas dance halls, go antiquing, etc. Greune and Fredricksburg are nice. There are also swimming holes like Blue Hole in Wimberly. You can go biking and see some Texas long horns. You can also get good BBQ. There is a town called Lockheart outside of Austin with a "BBQ trail" that is pretty famous.
Austin, of course, is very hip and there are good restaurants, food trucks, music, festivals, outdoor activities, Barton Springs pool, etc. so you can't go wrong.
I hope you have a great trip!