An anniversary week paced to two people's rhythm

My wife and I are going to Rome for our 15th anniversary, the last week of October — we land the morning of Monday, October 26 and fly home Sunday, November 1. It's our first time and I want it planned properly, not a listicle. We love beautiful old things, good food, and walking; we hate lines and tour groups. One night is the anniversary dinner — somewhere truly special, I don't mind what it costs, but I want to know exactly what it costs and how hard it is to get a table. The rest of the week we eat where Romans actually eat. For the hotel: somewhere small and beautiful near the old center, not a chain. Budget for the whole week all-in is around $9,000, not counting flights. We'd take one day trip out of the city if it's genuinely worth it. The important thing: we're booking everything ourselves — the hotel, the tickets, the trains, the tables. So the real numbers matter to us: what things actually cost right now, what's actually open that week, how far ahead the things that sell out need to be booked, and how we get in from the airport with two suitcases.