You can book excursions before you sail. The Royal Caribbean app will list the available excursions for your holiday. I can't remember how soon in advance all the excursions are listed but some (if not all) will be there already. They are usually more expensive than booking something independently but you have the reassurance that if something goes wrong and you are delayed your ship will wait for you. Check the web page too as I seem to remember that some might be listed there and not on the app.
There is a website called WhatsInPort that gives a good overview of the various ports you will call at. It will tell you how far away the cruise port is from the various towns - eg Piraeus is a good distance from Athens and you will need some form of transport to get to Athens itself - other ports it may be possible to get off and walk into the port to see the attractions. It's not the most user friendly website but it is very informative. You can use the information to decide if you want to just mooch around, book an independent tour (eg Viator for hop on hop off bus tours) or use a Royal Caribbean official tour. Some of the tours sell out really quickly and we recently had a tour cancelled and only found out once we had boarded.
If you are flying in then Royal offer airport transfers. We've used these and combined them with a tour on the last day to squeeze the last drops out of the holiday.
You can book the spa on board if you want to. They always seem to have loads of availability - just beware of the up selling for products if that's not your thing. The therapists usually have stands in a couple of places around the ship and you can speak to them about treatments.
The drinks packages aren't cheap but it's useful to know everything is paid for and you aren't faced with a massive bill at the end of your holiday. There are enough free options if you don't think you'll cover the daily cost but premium fresh juice, a couple of specialty coffees, a couple of sodas, two glasses of wine and a cocktail each day soon adds up. The free stuff is filter coffee, tea, water, lemonade and iced tea. A cocktail is $14 or thereabouts and a glass of wine is $11. Coffee, soda and juice around $3-4. If one adult in the room gets a drinks package then both adults have to have it. You can't use one package to get everyone a drink.
We have never used the internet package. Our last cruise was Greece and Croatia and apart from the last day we seemed to be near enough to land to get a reasonable 4g signal.
A couple of weeks before you sail there will be some additional info on the app. Things like dress codes for the various nights. There will be a formal night and probably a white night and some casual nights. There has definitely been a reduction in the number of people in tuxes/evening dresses since Covid - but it's great to get dressed up.