Nでも

an option, such as N

In an invitation or suggestion, noun + でも offers one possible example rather than insisting on that choice: "N or something".

Readings

How to form it

Put でも after the proposed noun. In a direct-object invitation it replaces を: お茶(おちゃ)でも飲(の)みませんか.
The invitation or suggestion supplies the context. The noun names one possible option, not an unrestricted "anything".

お茶(おちゃ)でも飲(の)みませんか。

Shall we have tea or something?

映画(えいが)でも見(み)ましょう。

Let's watch a film or something.

散歩(さんぽ)でもしませんか。

Shall we take a walk or something?

Contrast 〜ても / noun + でも: 雨(あめ)でも行(い)きます (I will go even if it rains). That describes an unchanged result, not an example option.
Contrast question word + でも: 何(なん)でもいいです (anything is fine). The positive-predicate guidance for that use does not rule out an invitation with ませんか here.
〜とか and 〜など can also offer an example in suitable contexts. They are overlapping ways to make a suggestion, not automatically incorrect alternatives.