Let's go. -- Ikimashou. 
Shall we go? -- Ikimashou ka.
Why don't we go? or: Would you like to go? -- Ikimasen ka.
Let's play tennis. -- Tenisu o shimashou.
Shall we play tennis? -- Tenisu o shimashou ka.
Why don't we play tennis? or: Would you like to play tennis? -- Tenisu o shimasen ka.
Why don't we go for lunch? -- Hiru-gohan ni ikimasen ka. NOTE: [Activity, etc.] ni ikimasen ka.
Shall we go for dinner? -- Ban-gohan ni ikimashou ka. NOTE: [Activity, etc.] ni ikimashou ka.
Let's go for a drive. -- Doraibu ni ikimashou. NOTE: [Activity, etc.] ni ikimashou.
Would you like to play (lit. go) golf together soon. -- Kondo issho ni gorufu ni ikimasen ka.
Tomorrow I'm going to Tsukiji, (but) would you like to come (lit. go) with me? -- Ashita Tsukiji e ikimasu kedo, issho ni ikimasen ka.
Where shall we meet? -- Doko de aimashou ka.
When shall we go? -- Itsu ikimashou ka. NOTE: No marker with "itsu".
What time shall we meet? -- Nan-ji ni aimashou ka.
Where shall we go? -- Doko e ikimashou ka.
Where shall we buy it? -- Doko de kaimashou ka.
What shall we eat? -- Nani o tabemashou ka.
Why don't we go to eat sushi? -- Shushi o tabe ni ikimasen ka. NOTE: [Thing] o [verb (pre-masu)] ni ikimasen ka.
Why don't we go see a movie? --Eiga o mi ni ikimasen ka. NOTE: When you invite s.b. to do s.th., it is best to use the negative form.
Why don't we go buy a souvenir? -- O-miyage o kai ni ikimasen ka.
It's noon already. Meaning: Let's go for lunch. -- Mou juni-ji desu yo. NOTE: Mou [time] desu yo. = Indirectly inviting someone to join.
It's that time already. (lit. Time is up) -- Mou jikan desu yo.
already -- mou
Yes, let's go. (accepting an invation) -- Ee, ikimashou.
That sounds good. (lit. That's good, isn't it?) (accepting an invatation) -- Ii desu ne.
All right. (accepting an invitation) -- Ii desu yo.
Well, let's see... (declining an invation) -- Sou desu ne. (in a negative tone)
Well..., now, it's not very... (declining an invatation) -- Ima wa chotto... NOTE: [Inconvenient factor] wa chotto...
It's inconvenient now... (lit. As for now, convenience is bad...] (declining an invitation) -- Ima wa tsugou ga warui-n desu ga... NOTE: [Inconvenient factor] wa tsugou ga warui-n desu ga... This non-acceptance is more direct.
Why don't we go for dinner? Now, it's a bit... -- Ban-gohan ni ikimasen ka. Ima wa chotto...
Why don't we go for a drink tonight? Let me see..., this evening; well it's not very convenient... -- Konban nomi ni ikimasen ka. Sou desu ne..., konban wa chotto...tsugou ga warui-n desu ga...
Where would you like? (lit. Which place is good?) -- Doko ga ii desu ka. NOTE: [Doko/nan-ji/nani, etc.] ga ii desu ka.
Any place is all right... -- Doko demo ii desu kedo... NOTE: [Doko/itsu/nan. etc.] demo ii desu (ga/kedo/yo)
What time would you like? Any time is all right... -- Nan-ji ga ii desu ka. Nan-ji demo ii desu kedo...
Where shall we go? Anywhere is all right. -- Doko e ikimashou ka. Doko demo ii desu yo. NOTE: yo is often added with this pattern
It's a little too early. -- Chotto hayai desu ne.
It's a little to late. -- Chotto osoi desu ne.
any time (general) -- itsu demo
any time (hour) -- nan-ji demo
any day -- nan-nichi demo
any day of the week -- nan-youbi demo
anywhere -- doko demo
anything -- nan demo
anybody -- dare demo
How about having pork cutlet? Yes, that's fine. -- Tonkatsu wa dou desu ka. Ee, ii desu. Or: Ee, kekkou desu.
All right, then let's meet at the station at two. -- Sore jaa, ni-ji ni eki de (aimashou). Note: When summing up, the verb is often omitted.
All right, (let's meet) in front of the Sony Building at 2:00 this coming Saturday. (summing up) -- Sore jaa, kondo no do-youbi no ni-ji ni Sonii Biru no mae de (aimashou).
Are you free tomorrow? Yes, I'am free. -- Ashita (o-) hima desu ka. Ee, hima desu kedo...NOTE: kedo is often added to make it sound softer
Do you have any (special) plan this coming Saturday? No, (I have) nothing special. -- Kondo no do-youbi wa yotei arimasu ka. Iie, betsu ni arimasen kedo... NOTE: Time (wa) yotei (wa) arimasu ka.
plan -- yotei
have (nothing) special -- betsu ni...(arimasen)
not yet -- mada
Well, not yet... -- Mada chotto...
next time (lit. again, next time) -- mata kondo
go ahead, please after you -- douzo osaki ni 
then, (I'll go) before you -- sore jaa, osaki ni