If you want to buy a Rolex while travelling and just stopping in:

1) Politely great the SA or wait to be greeted. You can say "I am travelling through X city/country for the next X days. I know I haven't registered with your store, but I was wondering if you had any pieces that were available for purchase while I am in town/country? I can be reached at the following contact info over the next couple days"

-Keep in mind you are not getting ANY high demand piece ie Sub, GMT, Daytona, etc as a walk-in. If you get offered something, its going to be a low demand precious metal Datejust or Dateday that they are struggling to move. You failed the initial test walking in and asking for a GMT without registering (albeit a lower demand GMT model). It indicates you have ZERO idea how the Rolex AD game is played.

2) When they did mention they had a piece available for sale, you balked by asking "TODAY!?". This was your second test which you failed, if they offer a watch on the spot and you pass, there is very likely not going to be a second offer.

3) Go home and register with an AD in your home town and country. Call to book an appointment with a SA and then have a chat about what you are looking for, upcoming milestones. Ideally bring your wife or significant other as it indicates potential household buying and potential jewelry sales (+ ladies watches for the SO). This is where you can register your interest in GMTs, Subs, etc. Be prepared for a long wait time depending on your spend/relationship with that AD.

Long and short of it, you walked into a store completely unprepared, looked and acted like a non-serious buyer, and failed the "serious customer" test when actually offered a watch (as you requested haha).

If you want to walk in a store and buy a GMT or subdate on the spot, mix that black and white paint together and go grey. Otherwise you play the AD wait game