Hilton and Century Hyatt has very frequent free shuttle going to Shinjuku Station. (JR & Subway). Century Hyatt's stop is right in front of Odaikyu Halc department store. The main Odaikyu store is next door. I personally think Hilton and Century are better choices than Keio Plaza as with Keio, your option would be either walk or take the subway for 1 or 2 stops to go to Shinjuku, about 140 yen each way I believe. They are also slightly better than Keio Plaza.

20000 yen is a bargain for this class of hotels in Tokyo. I am sure by now you get the impression Tokyo is not exactly a low cost destination.

Tokyo dont have Malls in the sense western countries have. The land is too expensive for Mall set up. Dept stores usually have over 10 floors for you to explore. Unless you are very rich, otherwise dont expect to be able to buy much in Tokyo. But window shopping is still a lot of fun. As for the electronics, Akihabara is the area to go. However, we found they are more expensive than in U.S. Unless you want the latest and stuff not available outside Japan, otherwise, it is not even worth the time to go.

Shops at Ginza are the high class stuff, such as Channel, Gucci etc The dept stores at Ginza also are of the high end. Shops at Shinjuku are upper end but not as high end as those at Ginza. Harajuku are more youth oriented, lots of fun shops. Ikebukuro has 2 biggest dept stores, Tobu and Seibu, and yes, there are a Gucci and some other brand names at the Metropolitan Plaza right next to JR Station. If you are really into shopping, then Ginza, Shinjuku and Harajuku are places must visit.

Do go down to the Basement levels of the Dept Stores though. They equal to our supermarkets. one floor usually completely devotes to food stalls selling all kinds of ready to eat foods. another floor devotes to fresh seafoods, vegetables, fruits etc. If you visit about 30 minutes before close, you will find amazing bargains. The freshest, cheapest Sushi and Sasami are to be found at the Dept Store basements 30-45 minutes before store close. 50% off most of the time. they must sell all stuff, no left over. Bakery goods as well. their breads are heavenly. Dept Stores usually close at 8 to 8:30.

Oh, btw, for the same kind of meal in many restaurants, lunch time is usually 30% less than dinner time.
during our trip, half of the time our dinners were the fresh sushi / sasimi bought from depart store basement. ;-)

For reasonably priced souvenirs, there are some very traditional, Japanese shopping streets at Ueno area. Ueno is at the Northwest side of Tokyo center. (Tokyo has 23 districts, Ueno is one of them). It is also a big station of JR Yamamote line (the circular line train at Metropolitan Tokyo).

If you only limit yourself to walking, you would severely limit yourself for places you can go, as well as make yourself very very tired. Tokyo's public transport is extremely convenient, the train and the subway. just bear in mind they stop running after midnight.

Buying a 7 day JR pass is probably one of the very few bargain travellers can find. the pass allows you take any JR trains, including Shinkansen, except Nozomi (the fastest and the most frequent one between Tokyo and Osaka). however, Hikari is only a few minutes slower than Nozomi in a 3+ hour ride between Tokyo and Osaka. The only inconvenience is Hikari only runs 2 times per hour, at :06 and :36. there is also another Shinkansen train called Kodama, which stops at every station therefore it arrives to your destination slower, but it runs 2 or 3 times per hour between the Hikari.

If you decide to get the JR Pass ( and I think if you ever plan to wander outside Tokyo to another city, you SHOULD GET the JR Pass), you must purchase it OUTSIDE Japan before you arrive.

You can now make reservation on the web even before you arrive Japan. Just make sure to mark you are Pass holder when making reservation. Also when you exchange your Pass Voucher to the actual Pass and get the tickets, make sure to give them the reservation references so they can link them together (to cancel your credit card guarantee).

There are ordinary car pass and "green car" pass. green car seats are larger and have a free drink during your journey. but for the difference of over 10,000 yen for the pass, i dont see its worth. the ordinary car is very comfortable, more comfortable than a business class plane seat.

Honestly, you do not necessarily need to make reservation. Because Shinkansen train has at least 5 cars that are for "non-reserved seating" (2 smoking cars and 3 non smoking cars). You can hop on the train and walk to these cars to find a seat. Car No.1 and 2 usually have plenty of seats.
We did our trip in first week of April. Eventhough we had made reservations, we ended up not use them at all, due to weather, or plan changes. The first time we went to the "Green Window" the JR reservation office at the station to try to change our reservation for a train 2 hours ahead of our original reservation, and was told the time we wanted was all full at the "reserved seating". However the staff told us we can try the "non-reserved seating" by directly going to the platform and try our luck. We went to the platform with about 10 minutes to spare. Train arrived. We went on it with many other Japanese who purchased the "non reserved seating" tickets (for them, reserved seat requires a surcharge) and we had no problem finding seats. One morning we got off our overnight train from Hakata (Fukukua at Kushu, the southern island) at Hemeiji (near Osaka), and were going to visit the Castle which is within 15 min walking from the JR station. It was raining hard. We decided to hop on Shinkansen back to Tokyo instead. Got back to the Shinkansen platform, with 1 minute to spare. We hopped on the Hikari, at car No.10 - reserved seating car, and started walking toward the car No.5. Before we even get to car No.8 the train was leaving the station. Car No.5 was smoking car. Car No. 4 was full. Car No.3 was also smoking car. but Car No.2 was 1/2 empty, and Car No.1 was 2/3 empty. So, unless you are travelling during Japanese national holidays, you really dont need to make reservations.

however, if you plan on taking any night train - then you must make reservation as they are quite often full. The one between Tokyo and Osaka is very popular, so as the one between Kyoto and Nagasaki (which we took, from Hakata to Osaka, very comfortable deep reclining seats).

do a search on google type in JR Pass, you will pull up all the info links you need.

Tokyo is probably the safest metropolitan in the world.

Singapore probably is the right place to shop, may even be cheaper than Hong Kong.