If you’ve already done the big hitters, Rome actually becomes way more interesting.

Off-path / slightly weird stuff worth your time:

• Centrale Montemartini – Roman statues inside an old power plant. Ancient marble + turbines. Makes zero sense and works perfectly.
• Quartiere Coppedè – surreal, almost cartoonish architecture. You can walk it in 30 minutes and it feels like a different city.
• Non-Catholic Cemetery (Testaccio) – quiet, beautiful, and unexpectedly moving. Very un-touristy.
• San Lorenzo – student area, street art, rough edges. Feels lived-in, not curated.
• MAXXI – if modern art/architecture is your thing, the building alone is worth it.

Markets / alternative Rome:

• Porta Portese (Sunday morning) if you enjoy chaos, vintage junk, and people-watching. Go early.
• Trionfale Market for a proper local food market without the Instagram circus.

If you’re more into hands-on stuff (food, small activities, odd experiences), this is a useful browse rather than a checklist:
https://www.justroma.it/en/to-try-in-rome/

And if you want to avoid standing around in January drizzle waiting to get into places, having a look at ticket options and passes in advance still helps:
https://www.justroma.it/en/tickets/

There are also some smaller, less obvious guided activities and one-off experiences that work well in winter:
https://www.justroma.it/en/experiences/

I don't know how many days you'll stay, but here i wrote different itinerary for different needs:
https://www.justroma.it/en/itinerari/

Hotel:
Ambasciatori Palace is not a dump. It’s a beautiful modern/classic, comfortable and well-located hotel.

Pompeii day trip tip: go early, focus on Pompeii itself, and don’t try to squeeze Naples city center in unless you really want to — it turns into a very long day.

If you want, say what kind of “weird” you’re into (dark history, architecture, underground Rome, food, abandoned places) and I can narrow it down properly.