Translation:Which events do you want to see?
It is already generally polite.*
There are various ways to make this sentence more polite, all of which head into the murky waters of keigo (敬語) or honorific language. The most polite version I can think of (disclaimer: I'm nowhere near an expert in keigo, nor am I a native Japanese speaker) goes something like: 「どちらの種目を見たくいらっしゃいますでしょうか」which essentially changes どの and ですか to their polite counterparts どちらの and でしょうか, and replaces 見たい with 見たくいらっしゃいます which is sonkeigo 尊敬語 (respectful language - for those higher in social status than you) of 見たくいます (lit. to be/exist in a state of wanting to watch).
An alternative which slightly changes the literal meaning of the sentece, but can still be used depending on the context is: 「どちらの種目をご覧になりますでしょうか」which translates to "which event will you be watching?" ご覧になる is the sonkeigo version of 見る. (Yeah, good luck figuring out that one :P)
Whew, keigo... this is the last lesson in the tree after all f(^_^;
Ah! You're quite right; I always forget about 二重敬語.
I actually haven't heard about ウ音便 before, so I don't think that it necessarily always needs to be used for verbs in keigo. Some quick research tells me that 「ご覧になりますか」is perfectly adequate keigo, though it doesn't sound formal enough even to many native speakers (hence to relatively common occurrence of the 「～ますでしょうか」二重敬語).
Oh that is interesting. As far as I'm aware, 覧 only has the connotation of "looking" or "observation", though according to my dictionary, it is often used in kanji combinations such as 展覧 (= "exhibition"), 総覧 (= "comprehensive summary"), or 観覧 (= "viewing"), which all have the connotation of getting to know something better by observation, whether that be by looking closer or wider.
I noticed you said the character in Chinese used to have that connotation, but does that mean it isn't used that way anymore?