OK... It's been a good week now and I have a few things to say. First off, unfortunately I did not get to play as much as I would have liked last weekend due to the timing of getting sick on release day. Still, I've got over 30 hours so far (and counting). I also have not finished a game yet. That is something on me as I usually start a game, make it so far, start a new game, make it further, start a new game, make it even further, etc. So far, I have played as America a couple times, making it to the Renaissance/Industrial era shift. Those were on standard speed large maps and 10 plus civs. My current game is Rome. It is on a standard size continents map with marathon speed and I think 10 civs. I have just reached the Renaissance era.
So, my thoughts are overall good. I like a lot of the new systems and changes. Districts are intriguing and there are several other aspects that I enjoy. Espionage, what I have seen so far, is a lot better than Civ V.
That all said, there are a few things, mostly minor, that I have as gripes. I have seen some complaints about the AI and some have even said that the AI is poorly programmed. I don't think THAT is the case, but I do see some glitches in the behaviors. I believe that is the main problem with it. I am also sure that it will be improved over time so I am not too concerned.
Speaking of glitches, some bugs that I have noticed include the production screen when a city has finished building it states at the top what was built. Only, it is usually "delayed" for me. If I build a Harbor, then build a Granary, when the Granary is complete, it states that the city just finished building a Harbor. That is a bit of a nuisance. There were other things, but I can't recall them at the moment. Anyway, I am sure that I am not the only one to address this.
Perhaps my biggest gripe and one that stifles my enjoyment to a degree is the build time. Everything just seems to take painstakingly long, especially for newly built cities. Districts are the worst of all. My suggestion would be to reduce build times for everything by about 5-10%. As it is, it kinda makes me lean towards Rome as I don't have to worry about the monument. One less building to build in my cities.
For Districts, I would like the removal of the cost hike every time a district is built. It really makes it hard to get later cities off the ground. I'm not trying to build every district in every city, but even two or three districts is difficult to do. I think that the best suggestion would be to instead have the cost for building districts get bumped up for each era. If you build 2 or 3 or 10 in a single era, they all cost the same, but when you go up in era, the cost is increased for newly committed builds. If you start building a District and the era changes before it is complete, the cost for THAT District should not be affected.
Anyway, those are some initial thoughts. Overall, I enjoy the game, the changes, and the personality. Don't tell my fiancée, but Cleo keeps flirting with me. She really enjoys my big... army!