I recommend doing it right after the grand entrance while your bridal party is still on their feet and everyone is standing up energized from the entrance.
I personally find it way more awkward that no one is looking at you while you dance. It's a moment that's displayed so publicly that not having people look at you while present would be so weird. The risk of having the dance anytime after food is served is that no one will pay attention to you because they'll be busy eating. Even if you go after plates are cleared, people are likely getting up to the bar, run to the bathroom etc. Having it right after your entrance ensures a captive audience.
Our DJ royally screwed up and didn't go into our dance after the grand entrance as planned. She starting playing the song and called us up during the second course so everyone was seated and busy eating and drinking. It felt so weird.
I'm doing mine right after our grand entrance before we sit down. When I've coordinated weddings before, even with an MC announcement - it's been annoying as hell for me to gather people and the bride and groom and say "leave the bar for the first dance!!" lol. SO I want to enjoy it and get it out of the way.
Ive seen it both ways, prior to dinner and after dinner.
My Brother IL did it before we even sat down, but its also just because of how their venue was set up, the dining area was small so the dance floor was kinda outside, so we all stood in the area, they entered, did their dance, and we all sat to eat. I actually found it quite sweet, as it felt more intimate to watch them dance.
My MOH did it post dinner, and she asked her bridal party (me included) to go up with our partners half way through the dance to make it a bit less awkward to dance after doing the father/daughter dances and thats what opened the dance floor for the night.
We did it when we entered. It made THAT way less awkward... But still horribly awkward lol and I love being the centre of attention 😆. It was a good break between cocktail hour and first course served. Got people moving too.
We are planning on doing our first dance after our grand entrance before dinner. We aren't doing a father/daughter or mother/son dance. Our first dance is the only formal dance so we are doing it before dinner then doing cake cutting after dinner then right to party time!!