How can I calculate the sun rising time for a specific point on earth?

Can I suggest Stellarium, which is a free planetarium program available for Mac OS, Windows and linux.

For any date, time and geographical location, you can obtain sunrise time and position.

To take account of mountains etc, there is the added option of including into Stellarium a horizon image. This will give you an idea of how mountains etc may affect sunrise time.

I rather think, however, that including a horizon image into stellarium might well be more effort than you intend to exert!

As a rough and ready estimation of the angle subtended by a mountain, estimate as follows from here:

You can estimate altitudes by extending your right arm in front of you, at eye level, with the hand bent toward you, and turned so that the palm and fingers are extended horizontally to your left. With the thumb held next to the fingers, so that all five digits are close together, the width of the hand is about 10 degrees. If you have a narrow hand, or a long arm, your hand may only cover 9 degrees, and a wide hand, or a short arm, may cause your hand to cover 11 degrees; but there isn't generally much more variation than this.

You can then use the sun altitude data from stellarium to estimate when the sun will appear over the mountain. You might also need a compass to orient yourself and your observations.

The Photographer's Ephemeris is the one that I use. It's quite practical and is an Adobe Air application.

I use it for the same reason that you mentioned and it hasn't failed yet no matter where I was.

It's available for iPhone, iPad, iPod Touch, Android system, Windows and Mac.

Desktop version are free but you do have to pay 5$ (Android) or 9$ (iOS) for mobile apps.

All these graphical tools are very nice, but you can simply go to Time and Date on the internet. There under Sun and Moon you can check for any time. For example, to see the November 2012 times for Vancouver.

Another way is to look at the weather on Wunderground. For example, the forecast for Vancouver shows the sunrise and sunset times.

Naturally this doesn't necessarily take in the mountains, but if you know there aren't any then this is a quicker way.

Failing that, I use terrain data in Google Earth, which is what we did to calculate where the eclipse would be in El Calafate, back in 2010. The eclipse was like 0.5 deg above the mountains, so we had to have it between the right mountains and be up a hill ourselves, to avoid having them block it. It was touch and go, for sure!