These are three great ways to make suggestions:

1) Why don't we / you / I + base form of the verb*
Examples:
▶ Why don't we go out for pizza?
▶ Why don't I drive you to the airport on Friday?
▶ Why don't we got out to dinner on Saturday?
▶ Why don't you call the movie theater to see what time the show starts?

* Note: The base form of the verb is the verb without any endings. Examples of verbs in the base form are: run, eat, play, go, find

2) How about + -ing form of the verb
Examples:
▶ How about going sailing this weekend?
▶ How about inviting the Smiths over for a barbeque?
▶ How about studying some French before our trip to Paris?
▶ How about getting Chinese takeout* for dinner?

* Takeout is food you order in a restaurant and take with you, to eat at home, in your office, or somewhere else.

3) Let's + base form of the verb
Examples:
▶ Let's take a walk on the beach.
▶ Let's work on the project tomorrow.
▶ Let's wait and see how the weather is before making our plans.
▶ Let's get tickets to a Broadway play.