The real world location of Akiba Dome
Ok, after re-watching it, at 6:28 of the movie,


   Umi: Why are we going overseas in the first place? If it's a concert, can't we just do it in Japan?
 Kotori: Remember what my mom said? A TV station over here wanted to do a report on school idols, so they gave Otonizaka High the offer.


So basically, they are in US for the TV station's offer and not for the third Love Live.

As for the location of Tokyo Dome, this site suggests that Akiba Dome is actually a reference to Tokyo Dome. The title in the site says

【劇場版ラブライブ】秋葉ドームはやっぱ東京ドームじゃね！？こことかモロじゃん！【僕光】(21:00)

The first sentence if translated into English means 

[Love Live the Movie] Akiba Dome is Tokyo Dome, right? 

Considering that the site is in Japanese (high probability of owned and maintained by Japanese community), and that they suggest that Akiba Dome is Tokyo Dome means that Akiba Dome doesn't actually exists in the real world.