Puglia Coastline

The train from Monopoli to Lecce stops near but not in Ostuni. I don't know if you can get a taxi from the train station, but I would think so. The historic center of Ostuni is one of our favorites in Puglia and it is an excellent place to stay and to eat --- we spent an entire week there in an apartment and there were great restaurants within a 5 minute walk. No cars in the old town because there are no actual streets, just narrow pathways and stairs between buildings. The regular town outside the historic center is full of things to do and places to eat and shops --- like many towns in Puglia, the center of Ostuni is "little" but the whole town is spread out around it.

Ostuni is not on the water, but a bit inland --- right on the coast, I only know about towns in the opposite direction to Lecce (i.e. between Bari and Trani).

I would consider Otranto and Gallipoli, but those are also places that are easy to visit from Lecce (not everywhere is), so moving may not be necessary unless you specifically want the different vibe in evening. I would not look at much smaller places because I think they might be too quiet--but I could be wrong about that until late October (my experiences were in late May). The coast from Monopoli to Lecce is not the best--look further south.
If you want one more base, I would consider somewhere in the Itria Valley because while day trips are okay from Monopoli, you could concentrate on zipping up and down the coast while in Monopoli instead (to places like Trani). I would be spending a lot of time on learning the bus and train schedule/routes for now. If you splash out for one driver/tour, I would consider that for the Itria Valley as you can see multiple villages as well as the scenery in one day. Maybe Martina Franca--I missed it but it's a good size city while still being charming.
Grottaglie will be nice--I managed to miss it twice! Don't totally discount Bari, if for example you need to stay a night for flight reasons--the old town is really quite lovely.

Our favorite was Trani, but we also liked Brindisi more than we expected to.

Thanks to all! Janet -- what did you like about Trani? And why did you like Brindisi more than you expected to? It's tempting since it's so centrally located but doesn't seem to have much to offer as a home base it seems.

Valadelphia -- is there enough in Bari to make it a few days stay? I'm not picky -- love old churches and little alleys and historic places and views.

I'm also considering Vieste since I have about a week after Monopoli and Lecce. So many options!

Thanks again for the feedback.

Yo JHO,
Gallipoli had the coolest vibe for us, but would def be smallish. Nothing wrong with that IMHO. We rented in Trani and enjoyed it too. It had what felt like the most authentic weekly seafood market, whereas Monopoli and Locorotondo seemed to vie for best overall sprawling markets (HUGE in both cases). Bari is a big city and held little appeal for my wife and I, except as the necessary train connection.
I am done. The end.

Nancy8 -- thanks for the recommendation of Ostuni. I know of it, but mostly as just a short day trip. If I meet some folks who are driving, maybe I can join them for a visit. Want to get in my 10,000 steps a day -- deal with the pasta, cheese, wine, etc etc etc! Thanks again.

Hey gregglamarsh --- thanks again for the feedback. Trani is coming up on my radar, so I'll try to check that out. Locorotondo, too. Glad to hear you liked Galipolli. Any special sights? Walks? Restaurants? Local places close by? I have a week at the end of my trip that I haven't booked yet, so I hope I can wing it a bit and plan on the fly. I find that there's a shortage of traditional hotels -- traveling solo I'm a bit skittish about staying in a 2-3 room B&B at the end a charming little street after dark and there's no one at the Front Desk. Been there, done that. So, that is my main challenge now. I've stopped worrying about depending on public transportation --- no car, no problem. Grazie mille!

Valadelphia -- is there enough in Bari to make it a few days stay? I'm
not picky -- love old churches and little alleys and historic places
and views. I'm also considering Vieste since I have about a week after
Monopoli and Lecce. So many options!

While I think Bari is underrated, it is also not in most people's top ten for the area. I think the old town is fantastic, but the main reason to stay there is for the convenience for day trips. It's a great place to start or end a trip, but there are small towns close to the airport. I never made it to Trani but hear only good things.
Vieste may be very quiet at that time of year--could you go there first? It is difficult transport-wise--so it does not get on many itineraries as a result. If you want to sit on a gorgeous beach, maybe do some boat tripos or hiking and little else, it would be a nice place to go. The bus trip is long.
I believe you are still looking for places to fill in your two weeks. Have you considered Matera? There is a direct bus from the airport if it fits your schedule. Two or even three days there would be great.

Trani just seemed more "real" to us, like it was set up for locals instead of for tourists. Brindisi, we happened to be there on some kind of holiday and the local families were out in force. This gave it a nice vibe, at least on that day!