@Rachael – My wife & I stayed in Nagoya last year and travelled in for the 3 days- Paul is right in thats its a well organised set up it still is not a “quick trip”. We stayed at the Hilton, about a 5 min cab (taxi) ride to the Merriot, where the train station is- first day was 2.5 hours from hotel to track!!! Maybe a bit of me being anxious and getting to the station over 30 min early! No need to, 30 seconds is fine. If you have a booked seat then there are no crowded que and shoving like the general train- but you NEED to book these seats before hand. We did in Nagoya a week or so before and could not find a way to do it in Toyko or Kyoto. My wife speaks Japanese (a fair bit but still struggles) and her friend currently living in Toyko and very fluent and both said you need to book from Nagoya station (seems weird to me!!). From the station in Suzuka its a 15-20min rough bus ride.
The key for the bus ride is to get the 3 days worth of tickets on day one, you then avoid the ticket line. There are cabs, but dont bother, not far to travel and slow, so no advantage there.
The bus will drop you a good 800m or so from the main gate- but I cant imagine a better walk into any circuit but maybe Spa or Monaco!
There are hotels at the circuit, but you wont get one. There are probaly 10,000 Japanese fans outside the Flower Garden (I think??) hotel where the drivers stay- the drivers all travel the 400m in cars, or they wont get there :) The fans here are awesome to watch as they get a glimpse of the drivers coming past- well worth a sit and watch for 10 min just to see their reactions!!
On Sat & Sun was probaly 1h15 – 1h30 to the circuit- much better. Knowing you can get there and get straight on and no bus ticket line up will say an hour. Getting home was hit & miss, but we missed our allocated seat every arvo but they still let you one with your expired ticket but you may have to stand.
We chatted a fair bit with team members from Red Bull, Mercedes and Williams. 2 lots stayed in Nagoya and the other about half way in a little town- cant remember the name but sounded like the teams had all booked up right away. So Nagoya probably your best bet and a great city- we found a Yankee pub around the corner- great spot !!
Hope that helps and have a great time !!!