Mmm, I think Criminal and Military both offer the opportunity to learn Martial Arts. It only fires if you haven't already learned the skill and I think it's random. Also it's just the one opportunity. I have never personally had the Nectar Making opportunity but I've heard it comes from Business. Don't quote me on that, though! You will need confirmation.
Mixology has opportunities, yes. To tend bar in this bar or that. Not sure if it has others, I don't remember but I did get that one a lot.
Riding has at least two: one where you meet other horse-lovers at the Horse Ranch and one where you receive "training" from an expert in the Equestrian Centre rabbithole. You must have the relevant lots for those to fire.
Charisma has several opportunities. One where you use the interaction "Get to Know", one where you use "Charming Introduction" on a stranger. Those are the two I remember now but I think there are others.
Writing has several opportunities, a few of which involve travel. You may have an opportunity to deliver a book to any one of the three travel locations. For this reason I would not recommend Writing for first generation, although it has been done (and well) before. There are also opportunities such as writing a biography of someone.
Inventing does have the SimBot chain but I can't remember if the different steps have different names. If not, they only count as one opportunity. There may be others but I don't remember what they are.
I hope this was helpful! Sorry there is so much I don't remember.
Edit: The following pages on the Skills section of Carl's guide include opportunity information.
AthleticCookingFishingGardening (Note: There are many more opportunities than the ones mentioned here)
HandinessPainting (Also includes which opportunity to avoid)
WritingAlthough not listed, Logic has a lot of opportunities, including simply raising the skill, tutoring someone, convincing someone that logic is good, going to the bookstore for various events, etc. Logic is a gold mine of opportunities.