I booked my ticket to Stockholm in November 2013 and I am planning a 11 days trip this time. I need some advice on Stockholm in general, and what are the nearby attractive cities that I can visit either via flight or train. I would prefer to use flight if the train journey more than 3.5 hours.

I am wondering if I should make a short trip to Tallinn or St Peterburg or Oslo or Copenhagen or any other good suggestion

Why November? I would check temperatures and daylight hours for that month before committing myself to such a trip. It makes for long evenings when the sun sets at 4 p.m.

I agree why go in November.

It does not make for good sight seeing when it is snowing or windy cold.

I understand that it is short daylight hours before making my booking. In fact it is from 1 Nov to 11 Nov. I am not aware that it will snow in November. Normally snowing start December right in Scandinavia?

I am from Malaysia which is Summer all year long, so definitely I will not choose a Summer vacation. I prefer Autumn/Winter which is totally different kind of cold weather

Many posters are not comfortable with travelling in winter. I'm not one of them, having spent the past winter travelling to Sweden on a regular basis and having spent an entire winter in Moscow.
The snow last November in Stockholm didn't start until the mid-end of November. There is still some snow around even today. In any case there is nothng wrong with snow, it doesn't stop anyone doing anything unless there is a blizzard. Sweden doesn't feel as cold as say the UK does because it is a dry crisp cold rather than damp cold, even in Stockholm. You just need to be prepared with correct clothing & footwear.
To visit St Petersburg you will need a visa & possibly for the other countries you mention. Is St Petersburg worth it-defintely. From Stockholm you can take a ferry to Helsinki for a short side trip.

Thanks Odin for supporting the idea of visiting Stockholm in November. I used to stay in Derry, Northern Ireland for like 2 months, and guess I am pretty fine with the weather.

In fact, I just back from Eastern Europe about 2.5 weeks ago, and there's still some snow around especially in Munich, Pilsen to Prague.

Lots of my friends informed me better to join a guided tour to St Petersburg instead of free & easy. Is safety an issue over in St Petersburg, especially towards Asian?

I Can recommend you to take a trip to Gothenburg during your stay in Sweden. I live there myself and it's a really friendly town with many things to do and explore. a trainride from Stockholm takes approximately 3 h and cost from 195 SKR (28 USD)