Hello! In my opinion, it would be better to use "usual" to describe the place that you are going to. The word "regular" would be better to describe the number of times that you go to the place - "I am a regular customer at the restaurant/pharmacy/market/bank"

Favorite, go-to, most frequented. I sent him down the restaurant I'd lately been frequenting to fetch me a steller rib-eye steak. Taste of Texas had been my go-to restaurant as a family-friendly steakhouse. McDonald's had been my favorite, most hung-out restaurant during my college days.

You can say either regular or usual. In the second half of your sentence, "tell them I want the same order" can mean either (1) "the same order as another person" or (2) "the same order as I ordered on a previous occasion". The way that I normally say meaning (2) is "tell them I want my usual order".