Getting to Shinjuku via Tokyo station on JR Lines is the simplest. But the transfer at Tokyo Station entails 10 minutes walk from the Keiyo Line platform to Chuo Line's with a help of escalators and travelators. It would take much more if you're a firsttimer.
The Keiyo Line train takes 20 minutes to Tokyo and runs frequently, then change to the Chuo Line train which takes 14 minutes to Shinjuku and runs very frequently. Total cost is 450yen.
Alternatively, if you are averse to a long walk at a busy station, catch the Keiyo Line train from Shin-Urayasu to Shin-Kiba, 10 minutes, 160yen, then change to the Rinkai Line which directly runs to JR Shinjuku Station every 20 minutes, takes 30 minutes and costs 540yen. So it costs 700yen in total, but it will liberate you from the possible hassle of changing trains at Tokyo Station. Transfer at Shinkiba is very simple.
You also have quite a nice walk once you arrive in Shinjuku to get to the Oakwood. Plan on at least 12-15 minutes, more if it's your first time. Any way you choose you will be doing some serious walking. Personally, I would recommend using JR to Tokyo Station and make the walk to the JR Chuo Line at Tokyo Station. As mentioned the transfer at Shin Kiba is easy (and Shin Kiba is a cool station with the wood accents) but using the Rinkai Line which morphs into a JR Saikyo Line train leaves you on platforms 1&2 at Shinjuku Station which is on the wrong side (east) and wrong end (south) of the station (farthest away from your northwest destination). The Chuo Line uses platforms 7&8 which allow you to exit on the north corridor with easy access to the west side of the station. You will be proceeding northwest of the station when you leave it.
It's only my personal opinion but I believe that platforms 1->4 which only have central and south corridor access are a little confusing to the first time visitor, especially if your destination is to the northwest end of the station. In other words, it's a little easier to get twisted around and confused, only slightly, but a little easier to get disoriented. Shinjuku Station is rather large and confusing. Just remember to bear north and west when looking for an exit and you should be OK.
Oakwood Shinjuku location:
I didn't know that the establishment was located in the extremely other direction. Actually it's very far from the Saikyo Line's platform, with maybe at least 20 minutes walk.
Although the opinion is different from mine, what Route246-san says is very persuasive as always.
I spoke to a rep at Oakwood, and according to him, Okubo Station on the JR Chuo Local Line is the nearest one from the apartment with 5 minutes walk from the south exit. No matter where you may change trains en route, Tokyo or Shin-Kiba, you might want to transfer again to the Chuo local train on platform #16 at Shinjuku. Okubo is next stop. It runs every 5 minutes in the daytime.
Getting out of the premises of Shinjuku Station is very challenging indeed for a firsttimer.
Actually, I made a small error. The Chuo Line from Tokyo comes in on 9 or 10 but everything I said is still consistent since 9&10 is closer to the west side than 7&8. I didn't know JR Okubo Station was closer. That means the Oakwood is pretty far from JR Shinjuku Station.
If you are going to JR Okubo Station you might consider transferring to the JR Sobu Line at Yotsuya Station instead of trying to maneuver Shinjuku Station at all. Between most of the line from Tokyo (actually from JR Ochanomizu Station) to Shinjuku, the Chuo (Orange) and Sobu (Yellow) trains parallel each other with the Sobu Line being a local train stopping at all or most stations and the Chuo Line stopping at very few stations. At the stations the Chuo Line stops, you can usually transfer by walking across the platform to the Sobu Line (and vice-versa). I'm pretty sure Yotsuya Station is one of those where you can walk across the platform to switch to or from the Chuo and Sobu trains.
Nah, since last November, platform #9 and #10 have been designated for Chuo Line Limited express Azasa and Kaiji. Now the westbound Chuo Rapid Service operates on #11 and #12.
Ok, on the assumption that OP changes at Tokyo, he or she might want to change from the Chuo Rapid Service to the Local at Ochanomizu, because the platform is the same and the opposite side each other and OP can avoid going up and down stairs or on escalators at Yotsuya or Shinjuku, though travel time will be added by 7 minutes on the local.
Isn't the change at Ichigaya inter-level? I can recall having to come out of JR Ichigaya onto the street near that bridge that crosses the Sotobori and then going down to the subway or am I confusing this with another station?
>>I can recall having to come out of JR Ichigaya onto the street near that bridge that crosses the Sotobori and then going down to the subway or am I confusing this with another station?<<
You may have made a detour and got out of the proper exit.
There is a connection gate on the basement 1 where only those who change trains between JR, Metro or Toei Shinjuku are allowed to pass. After you get off a Yurakucho Line train, instead of heading to the proper exit, go to the connection gate 'Norikaeguchi to JR Line' by escalator. then clearing the machine, go upstairs to the JR platform. Simple task.
I'm sure HJRH is getting intimidated reading you guys' posts:-)
This is not the cheapest option but I'd recommend taking a short cab ride from the Palm & Fountain Terrace to Urayasu Station on the subway Tozai Line, take the subway to Iidabashi and transfer to JR Sobu Line to Okubo.
I was considering the Tozai Line as an option and I'm glad you brought it up. But, I would take the Tozai Line to Nakano and catch an eastbound local from there back to Okubo.