Coastal Question

In 2015 I was able to get from Burgas to Nesebar and Sozopol (on separate days) by public bus. I can't tell you anything about bus frequency, though.

I'd recommend doing some careful research before choosing your coastal base(s). I believe there are rather a lot of tacky, low-end beach resorts in that area. The area was a popular destination for cheap sunshine before the Berlin Wall came down, and I have the feeling (yeah, this is not based on personal observation) the situation may not have changed much.

I was able to reach Sofia, Plovdiv and Veliko Tarnovo (also worthwhile) by public transportation. Trains, however, were very slow--not faster than buses; figure on about 30 mph. Your willingness to pay for private transportation, if necessary, may come in handy. It's nice to have that as an option if the public-transportation schedules do not align with your preferred itinerary. But you may be able to manage without it if you're patient travelers.

The towns of Burgas and Varna are iteresting but for me the most interesting and enjoyable was Nessebar. When I was there before the war there were a lot of russians and I would presume that is no longer the case so it might be even nicer now. The tacky end was Sunny Beach, not a lot of redeming value there. But Nessebar keeps calling me back. That and Provdiv. As much as I enjoyed Sofia I cant imagine staying busy for 7 days ... Veliko Tarnovo was another nice stop. And if you can find transportation look for Devil's Throat. Its interesting and getting there is one of those Death Road Trucker movies. You'll never forget it. Bulgaria is full of wonderful little villages and towns. Do the research or ask a guide, they are worth the stops. Love it there.

EDIT: The Septemvri–Dobrinishte narrow-gauge line. If you can link two stops with that its worth every second of the ride. I rode it from Avramovo to Bansko (yes, I did have to look that up).

EDIT, EDIT: and Asen's Fortress and Bachkovo Monastery and the Rila Monastery of course.

I just returned from a June 20-30 trip to Bulgaria, going to post my detailed trip report soon. We loved Bulgaria, and recommend all the places you are going to. I don't want to sound critical, but we had several days on almost the entire Black Sea coast and I have a lot of thoughts:

First, I wonder how much at the coast will be open in October and encourage you to research that. These are beach places REALLY focused on the beach activities. If you think Jersey Shore or Myrtle Beach in October...kind of crickets. My daughter was at an archaeological dig in Sozopol for all of June, and she said many restaurants didn't open up until the last week of June b/c beach season hadn't started, so I suspect by Oct a lot of places are pretty empty and cafes are closing. Museums definitely reduce hours by that point.

I don't think 5-7 days in any single one of those towns would be fun unless you planned a lot of day trips, which means transportation. Even the two bigger ones, Varna and Burgas, are quite small and very post-industrial (think: Allentown or Trenton). Varna is the least interesting, but Burgas Sea Park is really just a bit of walking, and in October you would not be hanging out on the beach itself. Nessebar is cute and historic but very small, a day trip. The roads along the coast almost all wind up into the mountains and back down to get to the next coastal town. I saw Flix buses and tour buses on the roads up and down the coast, but not a lot of scheduled city service, so getting between places might be pretty challenging. (FYI public transit in Sofia is EXCELLENT).

If you drive in your daily life, you could consider a car for the Black Sea portion of your trip and that would let you have two or three bases for a couple days each. We rented a car (from Avis at Sofia airport) for driving all over Bulgaria, and it was extremely easy. Roads were good, road signs in both Latin and Cyrillic, google maps worked well, and we were operating totally independently on our own schedule and able to make spontaneous decisions. We had a hybrid in the Toyota family, and only spent about $100 on gas for six days and a lot of driving.

You could do Sofia without a car, train or bus to Plovdiv, and then rent there when you leave for the countryside/coast, making a loop to return the car to Plovdiv. I would add, you do NOT want to be driving in the mountains at night - we were driivng in June with lots of daylight, but October is different. Roads were safe, but very winding and lots of trees to make them very dark.

If you use Varna as a base, you might consider a couple days to explore the coast to the north. In the north, we liked the undeveloped beach at Durankulak (almost to Romania) and the cute pocket beach in Kavarna, but check whether the really nice cafe at Kosmos campsite in Durankulak is open at that time of year and the hours on the Durankulak Archaeological site.

South of Burgas, we liked Sozopol, and if we'd had more time, we would have poked around the Strandzha forest. With a car from Burgas, you could go out to the Bulgarian military glory museum in Yambol (a very post-industrial economically struggling town but a great military heritage museum) - it's not far.

Both ends of the coast were, frankly, more interesting than the industrial middle cities.

Also, 5-7 days in Plovdiv seems like a lot unless you plan day trips. We did two nights, 1.5 days, and I would have liked one more day. I could see doing 3, maybe 4, nights if it's leisurely sightseeing. There were a few things we didn't get to in 1.5 days, but not much. However, I don't think there is enough there for 5 or more days. (We start early though - I'm ex-military). You could add Rila Monastery as a day trip - probably from the Sofia end, it's closer to that than to Plovdiv and there are great bus tours from Sofia.

Perhaps consider starting at Sofia to get an overview/context for Bulgaria before heading to the country?

Also re hired transport - I doubt you'll save money over a rental car for the coast/countryside portion, and you will have a lot less flexibility. It's not hard to drive there. WAY easier than LA or Chicago or pretty much any American city - these are mid-size cities of like 100-200K people. You definitely don't want a car in Sofia, but it was pretty necessary along the coast and between mountain towns. A lot of people who complain about roads in Bulgaria are either talking from decade-old experience, or have never driven the roads in Minnesota during spring rain/snow melt season (Bulgaria during dry season was much much better). Lots of speed traps and speed cameras though, so pay attention to that.