We are in Tokyo for just 2 nights. We have friends (distant cousins) who live in Tachikawa City.

They of cousre have invited us to their home to dinner , however, I am unceratin about the logistics of getting to Tachikawa (we are arrving to Tokyo by train from Kyoto).

We thought we would invite them to dinner in Shinjuku.

Two concerns: Would it be very rude to not accept their invitation to dinner at their home but rather invite them to meet us in Shinjuku for dinner ? ( I invited them first).

What restaurant can I suggest we meet at in Shinjuku that would be in nice surroundings and quiet so that we can linger to talk over dinner with excellent Japanese food ? Thank you.

I would have dinner in their home. This is obviously a big occasion for them and it's bound to be wonderful.

You should realize what an honor it is that they invited you to their home. This is somewhat rare in Japan.

Yes I do realize it is an honor to be invited.

How long does the train ride from Shinjiku to Tachikawa take ?

Would it be better to consider travelling from Kyoto to Tachikawa first, and then onto to Tokyo ?

Tachikawa is on the Chuo train line which basically runs from Tokyo station thru Shinjuku to Tachikawa.
There are express trains which skip some stations and regular trains. My memory is not great on this although I have taken these trains many times but I would guess the express train takes somewhere near a half an hour and the regular train maybe 10 minutes more from Shinjuku. You would therefore go from Kyoto to Tokyo, than to Tachikawa. Have a nice dinner and bring a gift from home.

Thank you for the wise advice. We will plan to take the Chuo Line from Shinjuku to Tachikawa. Since we are staying in Shinjuku this should not be difficult. It appears the train runs frequently into the evening. Returning home should not pose a problem. Could take a cab from Shinjuku Station back to Century Park Hyatt. Thank you.

I believe the Park Hyatt in Shinjuku has a shuttle to/from the train station but a taxi would not be very expensive. One note of caution is to note that Shinjuku station is very large and although I have used this station many times I always seem to come out of a different exit every time. I than look around to see where I am and make adjustments.

the Century Park Hyatt also has a shuttle every 20 minutes to and from the Shinjuku Station
Aloha!

Thank you for the shuttle suggestions.