The Royal Palace is part of the Imperial City. I think 2-3 hours to explore the whole Imperial City, with a stop in the Royal Palace as part of that time frame. There is an entrance fee that applies to the Royal Palace, which then offers access to the wider expanse of the Imperial City. As I recall, there is also a more limited section of the Imperial City where one can go in through a gate and behind the city walls without paying a fee. It was raining when we first got there, so I may be a bit fuzzy on some of the details because we hired a tuk-tuk and he took us around one area within the Imperial City (without an entrance fee), but then later dropped up off in front of the Royal Palace, where we did pay a fee before walking the grounds more fully (by then the rain had stopped). Hope this helps.