Hotel walking distance to Tokyo station

We intend to stay in Tokyo for 3 nights and the take the bullet train to Hiroshima.
Suggest a hotel (not an expensive one though) that is walking distance to Tokyo station or any station nearby

Not sure what "not expensive" means for you, but I always stay at the Hotel Metropolitan Tokyo Marunouchi. Very convenient, friendly and a much better cost-value factor when compared to the surrounding hotels:
https://www.booking.com/hotel/jp/metropolitan-marunouchi.html

If non expensive , you could look into a Toyoko Inn. I remember staying at one in Kanda that was quite close to Tokyo station.
But yes, there are other options. Have a look at any booking website.

The bullet train also stops at Shinagawa Station (in Tokyo) so you can expand your option to include Shinagawa Station neighborhood. If budget is tight, Toyoko Inn is good. There are Toyoko Inns near both Tokyo and Shinagawa Stations. I have stayed at both, and I prefer the Shinagawa branch (slightly).

to be honest, I wouldnt stay in either the Tokyo station area or the Shinagawa area for 3 nights. I would (and do) if it is only a night, but the areas around them arent very interesting IMHO, I would look to get off to Shibuya or maybe Shiba Park area if it is 3 nights and then just deal with getting to Tokyo or Shinagawa station when you needed to.

Lazy Pious (guest)

We thought that within walking distance to Tokyo station and where we stay there wil be good shoppoing malls to shop around. Just walk back to the hotel when tired and so on. Any area with acces to the Bullet Train is OK.

Yeah, look the area around Tokyo Station is quite business-y and p[ersonally I find it pretty boring. There are some shopping centres, but nothing exciting at all. We have stayed there quite a lot because Tokyo Station Hotel was one of our favorite hotels, and it is nice overnight and maybe a half day (maybe a walk around Imperial Palace), but more than that it is a bit of a yawn-fest.

If shopping is your gig, Shibuya is the place to be. We stayed a few times at the Dormy Inn Premium there which is great value and a nice hotel with a decent public bath. If you are lucky, you will get a view of the graveyard next door.

Shinagawa also has some up market shopping areas, but I found the area more chinese tourist oriented than western tourist oriented, we stayed at the Prince which was nice but it wasnt really geared up much for English. I'd only stay there again if I was getting in late and leaving the next day.

I would not pick either area for "shopping malls". Yes, Tokyo station has the large underground area of shops, but it's not like a big mall building like the suburbs or the one in Osaki.
As for access to the shinkansen, you're probably over thinking things. Any station on the Yamanote line (as an example) gets you to the shinkansen in under 30 minutes and most in 10-15 minutes. You would want a hotel close to to a station irrespective of where you stay, could be Shibuya, Ueno or even Asakasa-Mitsuke to name three out of dozens.
Three days in Tokyo should dictate your choice, not one trip to catch a shinkansen train.

I recently stayed near the Higashi Ginza subway station and enjoyed the area very much. You can walk to Tokyo Station in about 15 minutes, or to Shinbashi or Yurakucho in a little less time. If you have much luggage, the walk isn't very fun, but otherwise it is pleasant. If you do need to get luggage to and from Tokyo station, then it's a short cab ride.

Ginza these days has quite a few hotels that are not exactly cheap but not particularly expensive. Many of them are sort of "premium" properties of major business hotel chains, that were opened in the last five to ten years. I think you get more for your money there than you do at the hotels that are closer to Tokyo Station. And the transportation options are quite good.

Ginza has a lot of shopping complexes that aren't strictly speaking "malls," but pretty close. Of course, it has luxury boutique-type stores and two sizeable department stores, but it also has many practical places to shop, such as the Muji "flagship" store, a Loft flagship store, and the Itoya stationery (and much more) store. There is a new supermarket in the Maronnier Gate Building 2 that is the best supermarket I have seen in central Tokyo. There are also many good restaurants, a lot of them not at all expensive. It is fun to stay right in the middle of all of this.

The rooftop garden at Ginza Six is a nice place to hang out (and consume food and beverages purchased in department store basements; there aren't too many places where you can do this).

While being at a "walking distance" (<20 minutes?) of Tokyo Station sounds like a good idea on paper, unless you're staying right next to the station (and you can check the price of those hotels easily), it's much less expensive and just as fast to transfer from a nearby *JR* station.

The transfer between regular lines and shinkansen lines is easy. I haven't taken the shinkansen at Shinagawa station, but it is smaller so probably even faster.

/mellye
This what we have decided now. No need to be absolutely near the station.

I am thinking of Ueno, Asakusa, Ryogoku , Shinagawa areas. If there is shopping within walking distance of any of these- that will be a bonus.

I don't know any of those areas well (I am usually sticking to Shibuya and Ginza out of habit), but that's a no for Ryogoku.
Are there specific things you are looking for, or is it for window shopping?

Clothes and electronic gadgets

If you're looking for sporty casual wear, Akihabara is your go-to place since you want to shop electronic gadgets anyway.

Don't be afraid to stay a little further away from the train station. You can take a quick taxi ride from the station to your hotel. Japanese taxi drivers are honest and do not take detours that are unnecessary. Usually hotels that are very close to stations are more expensive. The cost of taking a taxi can easily be compensated by a cheaper hotel price.

Asakusa and Ryogoku will require extra transfers to get to the shinkansen or elsewhere in the city. While there is shopping in Asakusa, probably not what you are looking for. Ryogoku (stayed there a few times) - what shopping?? No. I also would not stay at/near Shinagawa. (Note, Shinagawa being a "smaller" station, it is still one of the five busiest stations in the world.)
Ueno would be a sensible option.
Also consider Shibuya - loads of shopping, or even Akihabara - not somewhere I would normally stay because it is so easy to get to while staying in the central city.

How is the area Hotel Nihonbashi Saibo - for shopping (perhaps can commute to Akiabara as well as Shibuya )?

Any place in central Tokyo is commutable, and from Hotel Nihonbashi Saibo, there are some direct trains that would take you straight from Ningyocho Station to Shinagawa Station (although if you wish to go to Tokyo Station you'd need to change trains). If you have luggage, be sure you find the correct elevator and the correct train.

If you explore the Hotel Nihonbashi Saibo area, you will find that it's a cozy old-town neighborhood with lots of places to have old-fashioned dinner. I don't think you'd find clothes shops, but of course, you can travel on commuter trains.

Regarding Hotel Nihonbashi Saibo, it is on the Asakusa line which is a metro line.
I prefer trains: they are closer to the surface, which means less stairs/elevators to take. But commuting by metro is totally fine as well.

By the way, when I say "train" I mean metro included.