Can you do anything before entering the Metaverse on a given day?

I'm still pretty early in the game, but things have opened up a bit and I do finally have freedom to choose what to do each day before going to sleep. I've headed to the Metaverse immediately a few times, and gone off to talk to people or make tools other times. On days where I choose not to go to the Metaverse right away, it seems like I can't go there at all.

How can I tell how long an activity will take before I do it? Are there activities I can do before I go to the Metaverse on the same day to try to maximize productivity for that day?

As long as you're not advancing time, you're free to do whatever you'd like. Things that don't advance time include the following:

• all activities inside the Velvet Room (including ranking up the Strength Confidant)
• visiting shops (but not working as a part-timer)
• talking to people and getting intel
• having your fortune told in Shinjuku
• meeting up at wherever the Phantom Thieves' HQ is
• (Sunday only) going to the Drink shop in the Underground Walkway (will give Charm and another social skill experience)

Things that will advance time, however include the following:

• spending time with Confidants
• doing activities (working as a part-timer, going to the Batting Cages, going Fishing, going to the Maid Cafe, studying in the library, working out at the gym, etc)
• going to the Metaverse (Palace or Mementos)
• going to Cafe Leblanc*

*the game will warn you, but going home before doing anything in an afternoon will advance the time straight to the evening, even if you haven't done anything yet

The likely reason you're unable to go to the Metaverse after doing activities during the day is that you're only able to go to the Metaverse during the day, not during the evening. And, as mentioned in this Q&A, going to the Metaverse will use up your evening, as well, until you can get massages.