You should divide two columns
(1) Things I have to do before I end my turn
(2) Things I want to do before I end my turn
Let's face it. Unless you're in a touchy diplomatic situation (i.e., you suspect an AI player of plotting against you), there's no good reason to check the Diplomacy screen and Foreign Stats and Reports every turn. There are a lot of screens that are just general "good to know" things that you don't have to check every time. The kicker there is, "the more you know, the more you grow." By taking a little time to just sit down and examine the galactic situation, you're going to learn some things about how the AI works and interacts and how the game is responding to your style of play. Eventually what you learn will become streamlined in your head, and you won't have to think about it so much anymore. Mastering the game like this can give you more time to do what you want during a turn as opposed to worrying about what you have to do.
My examples:
(1) Things I need to do before I end a turn
(a) Check the Planets/Ships screen to see if I have any new ships. I name them and then decide where they will work best strategically and send them there.
(

Check the Colonies screen and sort them by what they are building. !!!!!The usefulness of the Colonies screen cannot be overstated!!! You can instantly sort your colonies by any stat (Military, Social, Research, what they're building, what the shipyard is building, etc). By using this screen and sorting say.. what they're building, you can instantly see what colonies are building Nothing and give them a task. Let's say you want to build a Manufacturing, Research, or Financial Capital and want to know what colony is capable of producing the most. Just click the top of the proper column and you will instantly have every colony sorted with the one you want sitting nice and pretty at the top.
(c) Check Diplomacy screen every few turns to see how you're getting along with others.
Really, it's that simple in terms of "needs." Ships need to be sent places to serve their function. Colonies need to be set to build appropriate ships and buildings for support.
As far as things I "want" to do.. let's just say, it's a fun day when you can make every single AI go to war with each other on a 10 player gigantic map and still be Friendly and Warm with all of them.