My friend and I went out to dinner about a week after I was diagnosed, to Nandos (which are brilliant by the way because all of their carbs are available online). We were sat at a table where people were literally a ft away from me on both sides but I powered through, knowing that if I didn't do it then, I'd find it harder next time.
I injected 26 units that night... so it took a while... but no one noticed at all. Even my friend, who was sat opposite me, couldn't tell.
Think about all the times you've been out to eat before, have you ever noticed someone injecting insulin? It's just not something you look for unless you're diabetic yourself.
I think injecting in the belly is much easier when out and about although I have heard of people injecting through tights if they want to wear a dress, so that'll be one to try in the future!
So don't worry about it and just remember that everyone elses body is doing the exact same as what you're doing to your own.