We wouldn’t recommend any stiletto heels! You may sink in the grass. Any high heels with a wedge or a chunkier heel would be great. But that’s the only thing we don’t recommend! Wear whatever shoes make you feel comfortable & confident!
If you have a plus one you may! But if you do not & it’s a last minute thing, there likely would not be any accommodations for your date (food, seating, etc.).