How is Prague in November around 14-20 and how many days do you need ?
I know its cold, but not sure whether its rainy and open to tourists during that part of year ?
Prague is beautiful anytime! I think it's one of the most beautiful places in the world! November shouldn't be too cold but you will want a coat. Be sure that you are prepared to walk and do a lot of inclines around the castle area from the old town area. Enjoy!
I live in Prague and there are tourists over whole year. All museums, sights etc. are opened over whole year, however in November there can be shorter opening time at some sights.
Now I got in mind, that for example Valdštejnská zahrada | Wallenstein Garden is opened only from April to end of October. And I think that some other public gardens can be closed, but I think it is not the best part of Prague, even it is nice to see.
You should know, that in November we have around 9 hours of day light (you can walk in city after sunset for sure and all sights are nicely lighten) and temperature is around 0-20 celsius (I would bet It will be around 10). And it is kinda rainy, but with umbrella you should be ok, depends how high comfort you like. Usually we have two types of rains here - fast which can make you really wet, but usually not longer than half of hour, and long which can continue over few days (with stops) but you can walk in it with umbrella without any problems.
In November many people goes to Prague mainly cause of low season - which means less tourists. Prague center has narrow streets so at high season it can be sometimes crowded.
Btw we have friendly pubs with awesome czech beer which make you smile at any time of year:)
The season no good in November, best to go to Prague is spring.