I should probably also add that I am trying to do this on somewhat of a budget- would love to keep it under $800 for the 8 days (not including accommodation and the cooking classes).

We had 6 days in Sorrento, staying in an apartment and loved it. Day trips were easy, even though we did get off at the wrong bus stops once or twice. It just meant we explored an area we didn't mean to and bought another bus ticket to go to where we really wanted to be.

You can book a tour to Capri but we just walked down to the port, there are some steep steps we found, and bought a ticket on the next ferry leaving for Capri. It was quite cheap from memory. Once on the island, there are buses to get around.

You can get the bus to Positano, Amalfi and Ravello. The train goes to Pompeii. There are other small coastal towns as well. Don't forget to explore Sorrento, we liked it as a base, it is quite touristy but that never bothers us (after all, we're tourists) and the views are wonderful.

If you get out early and don't need to be back until 4pm, you have nearly a whole day but when we were there, the buses did get very busy, with lots of people standing, so don't wait until the last minute to head back to Sorrento.

Kay

Forgot to add - you may meet up with others at the cooking class who'd like to do something one morning with you.

And if you don't know any Italian, learning basics like one, two, ticket, one way, return, train platform, thank you, please etc, will go a long way.

Have fun. The cooking class sounds great.
Kay

Thanks, Kay! Anyone else?

It is typical of many cooking schools in Italy that they incorporate a lot of organized sightseeing for their students as part of the courses. So you might want to check with them.

The fact that your classes are in the afternoon is going to limit how far you can go when you are relying public transportation. Pompei is a huge site, so you need to wait until your classes are over if you want to explore it without feeling frantically rushed, but before your classes are over, you could easily take the train to Ercolano and see the suburb of Pompei that was wiped out in the volcanic eruption. It only takes about 90 minutes to tour fully, and it is an extremely fascinating ancient town frozen at just that moment of its ending.

Transportation between Sorrento and Naples is constantly available, and if you have any interest at all in Italy and European history, I highly encourage you to visit Naples, especially for its archeological museum, which sounds boring but I assure you it is not. With an early start, you can visit and be back to Sorrento in time for your class.

Naples has a fierce reputation for abrasiveness, dirt, chaotic traffic and petty theft and I am not going to tell you it's all a fairytale. But it is much more bark than bite, and with a good map and guidebook, and a level head, you can confidently make your way to the great sights of Naples, which is an astonishing European city.

If you are at all interested in European painting, the Capodimonte museum in Naples has one of Europe's most compelling collections, so that is another option (but you cannot see both the archeological museum and the Capodimonte museum in the same day and be back to Sorrento by 3pm.

I hear you that you are on a budget, but if you were at all nervous about moving around Naples using public transport or just your feet, taxis in the city are metered and not extravagantly priced. (It is quickest to take a taxi to the Capodimonte museum.)

If you are interested in food, a trip to Naples for its markets and its pizza and pastries alone is something you might not want to miss, and your cooking school should be able to give you the best guidance about that.

I don't think you have made a mistake renting an apartment. You will have your own kitchen, and produce from the region is great, and so are breakfast treats you can enjoy without being stuck with hotel hours. Were I in Sorrento for a week with my mornings free, I would probably take a flyer on using the local buses or trains to visit the areas of Sorrento that are just outside the tourist area. There are beautiful lemon groves ringing Sorrento. There is a tiny beach community (Meta di Sorrento) that is 5 minutes away. There are pretty walks everywhere that most tourists never see.

I agree that some of your cooking class mates will be up for excursions. If others are interested in Naples, you might go together and split the cost of a taxi to the Pignasecca street market or other sights of interest.