hi Chad, I agree with Eddie. Here's some addition to the answer:
In your case, if we bring up a suggestion of going to a place and performing an action (in the place mentioned), we see the action is the purpose of going there. So it would be "Shall we go to the restaurant TO have a meal." Thus in Chinese we just don't say the "to". Instead, we put two actions together because from the meaning people automatically figure it out.
More examples:
Wǒmen yīqǐ qù tàiguó lǚyóu ba. (Let's go to Thailand and have a trip.)
Wǒmen yīqǐ qù diànyǐngyuàn kàn diànyǐng ba. (Let's go to the cinema to watch a movie.)
However, if you'd like to stress the two actions happen one after another, it's suggested to use " ránhòu", meaning "then", written in Chinese as 然后。
examples:
Wǒ tuīkāi le mén, ránhòu kànjiàn le tā. (I opened the door, then I saw him.)