Why do most anime have field trips to Kyoto? Most of the anime and manga I have read/watched have featured a field trip to  Kyoto. (As a related example, Beelzebub's field trip destination was Okinawa.) I don't know much about class level or the education system of Japan.

Is Kyoto a field trip destination in the Japanese education system or is it just a trope?
Actually it's not only Kyoto. Depending on the manga's theme, the field trip could be anywhere, but yes, most of the time it'd be Okinawa, Hokkaido, Kyoto and Osaka. As a side note, most of the manga I read has the school trip to Okinawa and Hokkaido instead of Kyoto like yours.

Okinawa is usually visited during winter because due to its geographical location, it is warmer than the rest of Japan. Example for manga that has summer in Okinawa is Great Teacher Onizuka.

Hokkaido is the other way around. It is usually visited during summer for the students to enjoy cool summer holiday swimming and all.

Well, Okinawa and Hokkaido is usually interchangeable, depending on the author. Okinawa is also visited during summer if the author wants a hot summer holiday theme. Hokkaido if s/he wants skiing during winter.

Now, for Kyoto, they are visited for the obvious reason. Kyoto was the old capital of Japan. It was referred like a holy city, much like Vatican is to the Catholics, while also was the central for administrations and home to the Emperor. It also hosts the famous Honnoji temple, albeit the location is not the same as the Honnoji where Nobunaga met his demise.

Osaka is also sometimes visited, thanks to its culture. Osaka is famous for its Kansai-ben (Kansai dialect) and the Osaka castle, of course. Osaka is also home for many famous Japanese artists and bands, like L'Arc~en~Ciel and SCANDAL. Ranker listed at least 25 of them.So, that could be one of the reasons too.