October 2022 Honeymoon – suggestions, comments, and opinions welcome :)

My fiancé and I are getting married 10.09.2022 and want to go on our honeymoon after for a week or two. We've brainstormed a couple ideas and I'll list them below and if anyone here has experience going to these places or doing these things, please let me know what you think/what we should do! I also feel it necessary to mention we live in north-eastern USA.

1. Italy. We aren't tied to any specific part of Italy but it's my dream to go there since I was young. Neither of us have ever left America but this feels like THE chance to go.
2. NYC. I know that sounds odd but we fell in love in high school theatre. We were thinking of seeing a Broadway show each night, as well as exploring the sights and restaurants.

I'm very open to suggestions within these options, and things you may have researched or done yourself we may like. We are beach people, foodies, theatre kids at heart. Thanks for your help friends 🙂

EDIT: didn't think to mention our max budget is around $5000. We've been looking a lot on Airbnb and such, but we're not sure what international airfare looks like.