1st Time to Japan

I will arrive Haneda 2305hrs this end of Sept, I will need to attend an event in Big Sight Tokyo pls tell me
1)which Toyoko Inn to book as there is many and in all different location I don't know, Which of these hotel will be the most practical for me to stay for this trip?
2) what are my transport option since i arrive late and how much? Please help!

If you can catch the last train on 23:59(weekday), Tokyo Shinagawa Aomono-yokocho-eki should be nice.
http://www.toyoko-inn.com/e_hotel/00049/index.html

The last train takes you there(7th stop) without any transfer.
next morning, you can catch the direct train to Kokusaitenjijo(means "International Exhibition Hall") station at Shinagawa Seaside station, 10 walk from the hotel.

thank you very much for your kind answers! I was panicking as i didn't have the slightest idea on which one toyoko inn to pick. Please pardon my ignorance but i must ask the following

1) if this would also be another option to stay at Toyoko Inn Tokyo Shinagawa Oimach?
http://toyoko-inn.com/e_hotel/00146/index.html

2) Though i will be arriving on a weekday, if i miss the last train would there be taxi's available? any idea how much it will cost?

3) how much is are the train rides to big sight? any idea?

If you miss the last train, there are two Toyoko Inns right near Haneda. A taxi to them should be around Y1000, much less than to the other one.
http://toyoko-inn.com/e_hotel/00042/index.html
http://toyoko-inn.com/e_hotel/00068/index.html
If you will be going back and forth several times to the Big Sight, you should transfer to the one "by..." suggested. The fare on the TWR subway he suggested will be Y260 or Y320.

About the taxi. Print out the Toyoko Inn page to show to the driver.
Do NOT try to close the taxi's door. They are automatic, controlled by the driver.

... : If you can catch the last train on 23:59(weekday), Tokyo Shinagawa Aomono-yokocho-eki should be nice.
The last train takes you there(7th stop) without any transfer.

This departure time of the weekday train is for the other Keikyu station in HND, which is in Domestic terminal; the train is scheduled to depart from the station in International terminal slightly later at 00:01.
Aomono-yokocho will be the 8th stop after HND because the train is an airport express.
The fare is 400 yen per adult and the required time is about 20 minutes.

which Toyoko Inn to book
I will arrive Haneda 2305hrs this end of Sept
Though i will be arriving on a weekday, if i miss the last train would there be taxi's available? any idea how much it will cost?

It seems that in and around HND terminals there is no Toyoko Inn hotel.

Toyoko Inn has two hotels ("Haneda Kuko No. 1" "Haneda Kuko No. 2") located closed to a nearer Keikyu station Otorii, which are mentioned by Dick H.

If you book one of the two hotels but don't catch a right train or a courtesy bus (due to delay in flights for example), it's highly likely you will have to have a taxi ride.

I suppose the taxi ride will cost over 1000 yen, considering that a high rate is applied during 10 pm - 5 am.
On a map the two hotels appear to be at least 2.3 km distant from HND International.
The fare is estimated at 1610 yen if the distance is 4 km, at 1250 yen if the distance is 3 km.

Courtesy buses will be available to the two hotels; they are scheduled to depart from the bus stop around a waiting room for group-tour buses in International terminal
at 23:12, 23:32, 23:52, 23:57 and 00:12.
http://www.toyoko-inn.com/hotel/00042/shuttlebus.html

The last 00:23 Keikyu train for Otorii, which is the last among all trains of a weekday, is a local train. Otorii will be the 3rd stop after HND.
The railroad fare is 280 yen per adult and the required time is about 5 minutes.

if this would also be another option to stay at Toyoko Inn Tokyo Shinagawa Oimach?

Well, if you have enough time you can get to Oimachi making one transfer from Tokyo Monorail to JR-East.
But I suppose in a case where you can catch the last 00:10 monorail train, you can catch either the last 00:12 courtesy bus or the last 00:23 Keikyu train of the weekday for Otorii.