Which Chinese Historical Drama Should I Watch Next

I loved 3 of the dramas from that list. I think The Story of Ming Lan probably fits your description the best. The female lead is very smart. She's very observant and knows how to navigate through situations since she was a little girl. There are scenes that take place in the palace, though it's not as much as you would think because she's a court official's daughter and not royalty. 

It seems you like comedic dramas at least judging by your love for Go Princess Go and The Romance of Tiger and Rose. You should check out The Story of Yanxi Palace. The female lead is a bit of a reversal character seen in palace dramas. She's kind of the character you would expect to be the villain because of her face. The drama has sad moments, but there's hilarious ones too because Yingluo (the female lead) is not a pushover and has no filter sometimes! This is a palace drama so Yingluo doesn't really get to leave the palace though.

 NightTraveller:

Most of these dramas had great reviews but as someone who loses interest very quickly I need a drama that has a strong first couple of episodes. I need a drama that has both smart characters (including the FL) and villains. I need a drama where the setting takes place both inside and outside of the palace.

 something:

I think The Story of Ming Lan probably fits your description the best.

The Story of Ming Lan fits most of what you're looking for, but definitely not the "strong first couple of episodes" piece. The first episode is a bit confusing for a first-time watcher. Then there are some decent episodes of the leads when they're kids. Then many, many episodes where the leads are young adults but we are shown the leads' obstacles, poor choices, and time-wasting romantic story lines with other people rather than the leads at their best (that comes later). It wasn't until about 25 episodes in that I finally was sure that I wasn't going to drop it, because things started to pick up at that point. Even if you skip parts, the first third of the drama requires a lot of patience!

 something:

The Story of Yanxi Palace. The female lead is a bit of a reversal character seen in palace dramas. She's kind of the character you would expect to be the villain because of her face. The drama has sad moments, but there's hilarious ones too because Yingluo (the female lead) is not a pushover and has no filter sometimes! This is a palace drama so Yingluo doesn't really get to leave the palace though.

I agree with all of that. The romance is very, very slow burn (the romance doesn't really start until the second half of the drama), but I'd still say that the first few episodes are strong and do a good job of pulling viewers in. 

 NightTraveller:

The Story of Yanxi Palace sounds the kind of drama I’m looking for with a strong FL who doesn’t get pushed around. As long as the drama has strong dialogues (like what I saw in Scarlet Heart) then I don’t mind if majority of the show takes place within the palace.

Yingluo is definitely a strong character who always manages to get her way in the long run. And yes, there's good dialogue.