Its fine to bring your own bottle of alcohol for consumption in your room as its a private domicile. You can go as far as to ask housekeeping to remove the items from the honor bar which is what I do and put whatever it is you want in there.

Now at restaurants be prepared to pay the corkage fee if you don't want to then enjoy your cocktail before going out to eat. I feel paying the corkage fee is worth it especially if it costs $30-$80 for a bottle of wine. If I have a $20 bottle of wine and its $10 for corkage thats fine because the $30 bottle of the house wine could be blah. Even if the corkage fee equaled the price of the bottle at the restaurant i know that I will enjoy the bottle more since I'm familiar with it. This is not to say that I would try restaurant wines if its a good restaurant.

I agree that its a good idea to BYOB rather than pay the high fees of the hotel.