European Honeymoon with History & Beach Days… in October through February?

Searching through the millions of other posts here, but would greatly appreciate any assistance.

We get married in September and have not planned a single aspect of our honeymoon thus far. I would love to take in November, but am not sure if that's pushing it weather wise.

Info: – Flying out of Detroit – Aiming for 2 weeks – English speakers (I speak and understand Spanish well enough to have awkward, but friendly conversations… but I think the credit for that largely goes to the unanimously generous Spanish speakers I've encountered. I've heard Spaniards are less forgiving lol) – We're early 30s, looking for romantic day trips and evenings more than clubs or raucous nightlife

I'd looooove if someone could confirm if the below is possible in Spain or Italy, but open to alternatives if the answer is no.

Really Want to Haves:

• Transportation: Safe & easy to get around by walking or public transport. Don't want to deal with car rental or driving. Walking-heavy places welcome!

• Budget: Under $10k. If we could do it under $7k I would be thrilled.

• History: museums, architecture, the ability to just feel it throughout a place

• Food: we're adventurous eaters and love a good meal. I would love a place where the food is superb without breaking the bank for fine dining.

• Nature: Greenery & beaches! Casual hiking, different geographies (hills, water views, etc) would be lovely

• "Authentic" or not very superficially touristy. I'm a bit of a hypocrite in that I want spaces that can accommodate clueless American tourists without being surrounded by or solely in places that are designed to cater to clueless American tourists.

• Climate: sunshine and weather warm enough for a day at the beach and a suitcase with nothing warmer than a light sweater/jacket.

• Minimal to average harassment: fine with panhandling, just want to avoid the targeted, follow you down the street, you're American so you must have money variety if an area is known for it

Also, is a travel planner worth it? If so, what did you pay and did you feel they added to your experience or saved you money?