“Looking forward to eating” is correct here.
“Looking forward to” is acting like a phrasal verb that wants a direct object — a noun.
I am looking forward to the test
She is looking forward to the new “Star Wars” movie.
They are looking forward to a better future.
We are looking forward to running a marathon.
I was looking forward to eating at the restaurant.
You’re right that “to” usually takes an infinitive verb.
I want to run a marathon.
Some verbs can take either a noun, a gerund, or an infinitive verb as their “object”.
I hate to run.
I hate the test.
I hate running.
Many very simple (usually 4-letter) verbs work this way:
- I want to swim,
- I love to swim,
- I like to swim,
- I plan to swim,
- I need to swim,
- I intend to swim
while other verbs do not:
Unfortunately, “look forward to” is a verb that doesn’t work this way. It requires only a noun or a gerund.
Yes: I look forward to running (the race).
Yes: I look forward to the race.
No: I look forward to run the race.