thadiusdean,
I play with the "minimize pop-ups" that CCRunner7 mentioned, and it does a lot of what I want it to do. However when there is that once-in-a-while turn that I have no units to move, all of the pop-ups will still happen right away. If I want to do other things, or simply "look around" as you stated, I will choose any non-worker, non-settler, non-granary, non-limited supply building/project, non-curency/culture/research to build, and do what I need before changing back the city. If you do this, don't forget to choose the proper item to build less you build something silly!
Also, note that there is a bug in this feature. The pop-ups happen on the "start" of the turn, and do not update accordingly. This means if you have 4 cities that are scheduled to pop-up at the end of your turn, when you reach the end of your turn, you can make all 4 of them build a Jewish Missionary...even though there is a limit of 3 on them. Also, another annoyance (could be considered a bug) is if you're in city 1's (of 4) pop-up screen, and select "examine city..." and [Escape] out of the city without selecting an item to build, you will switch to city 2's (of 4) pop-up screen. This will continue until you [Escape] or select build items for the rest of the cities. When you get back to city #1, it will no longer say "$CITY has just built, what would you like to work on next?" Instead it'll just say "What would you like to build in $CITY?"