Southern Spain 10 days late October early November

Southern Spain (Andalucía) can still be very warm in September, so late October is probably better.
10 days is perfect for the classic Sevilla-Cordoba-Granada trilogy. With a few extra days, you could spend some time in Madrid, since you are likely to transit there anyway.

Assuming Madrid flights, a possibility could be to head straight to Córdoba upon arrival, spend 1-2 nights, then 2-3 in Granada and 4 in Sevilla, and a final night in Madrid before your flight.

If you find good flights to Seville, you can skip Madrid altogether. Cádiz is a lovely additional destination in the region, and if you are willing to rent a car the white villages around Ronda deserve 1-2 days of exploration. Some people also like Málaga - my memories are hazy, I remember an enjoyable old town (many of those in Spain...) but I am not sure how to rate it.

Look at flights out of Newark also.

I was there for 3 weeks in that time frame. I was able to fly to Granada as a code share. It meant a transfer in Madrid, but saved the hassle of getting around a new to me Madrid to find the trains, etc. Then Sevilla, Cordoba, Toldeo, Madrid, Valencia, Barcelona airport.
2017 was a drought year and the normal rains had not started yet. Spain has really been affected by global warming, so it way still be warmer by end October. Find a website for historical weather data, that includes precipitation, and review the temps and rain for your weeks for the past 5 years. That will give you a current picture. Granada was still crop pants and sandals, but by Nov 9, Madrid Saint's Day, I needed a beanie and gloves to watch festivities in the Plaza Major....then there were snow flurries in Segovia on the 10th, but snow free and sunny on the 11th. Sidewalk lu ches were feasible everywhere but Madrid.
Sevilla has a large park with gardens...Parque Reina Sophia...built for some international expo type thing in early 1900s. There are gardens in the Sevilla and Cordoba Alcazars. Casa de los Duenas in Sevilla is a house museum with garden. The gerenium patios in Cordoba are much less obvious, but there are still some displays on short alleys.
I stayed in the museum area of Madrid as it is also close to Atocha train station. There is a cute botanical garden next to the Prado Museum and Retiro Park is a massive greenspace a pleasant walk from there.

I loved the gardens at Palacio de Viana in Cordoba.

balso has given you a good general itinerary to start with. You will need to decide on flights to figure out a more precise itinerary.

And there’s no need to reinvent the wheel - there are many threads on the Spain forum for Andalusia to read that would probably help you narrow down what is generally recommended, what YOU want to see, how long you want to stay in each city, and how to go about it. Some stops vary by interest.