I withdraw any support for 'arenas' or 'battlegrounds' in #eveonline, it already exists in RvB. Holy shit this owns.
He brings up a great point that I think is lost on many players. In EVE most thing that are in other games come about as a mechanic, are player driven. There are no set arena's in EVE. However there are lots of Arenas.
For me an Arena is a place you can go to get some mostly consensual PvP action without much effort. Grab a rifter or other ship you are willing to loose, and head to any of the following places and you will inevitably get a fight. Obvisouly RvB is effectively an arena setup in high-sec and provides quick PvP. However if you are looking for something different there are many other easy places to find pvp.
Arena #1 Amamake: Upon arrival in the system warp to the sun at 0. You have about small chance of landing on a fight. Then use the directional scanner to scan down each of the planet clusters. Look for comparable ships like Rifters, Merlins, Incursis and Punishers. If flying a T2 frigate look for these plus destroyers and other T2 frigates. Warp to a belt when you find something. If nothing there stay for a 30 seconds or so then warp back to sun. Great practice for directional scanning. You will almost always get a fight within a few minutes. Typically, about 50% of the time, the target will have one or two ships backup that will arrive soon after fight begins. Also check out nearby Auga and Dal.
Arena #2 Molden Heath (Bosena/Heild). Expect several small pirate gangs to be operating with cruiser and under sized hulls. Gunboat Diplomacy and Black Rebel Rifter Club are very active and will engage any small target very quickly. In addition there are several other groups operating in the area plus tourists. The static plexes in Heild are more often then not the main spot where fight occur. Check Sard Caid's feed which may be active and is a great source of intel. In general major pirate corps in area will accept and honour 1v1s. Molden Heath lowsec forms a nice loop that is great for a quick roam.
Arena #3 Hevrice: Home to Tuskers PvP corp. In addition there are several other entities in the area. Check out Hevrice as well as the several adjacent lowsec systems looking for pirates.
Arena #4 Tama: Like Amamake this system usually has several active small gangs and solo roamers at any one time. Warp to celestials scanning down potential targets. You won't be disappointed often.
Arena #5 Syndicate: This entire region is populated by many smaller alliances and corps specializing in small gang pvp without the burden of sov warfare. Small gangs are the norm but solo fights are still frequent. Be prepared to deal with bubbles and the occasional hot drop. Best region to roam in if you are in a small gang yourself. Lots of stations for 0.0 that are NPC so you can dock. I prefer to enter from the Harroule-MHC-R3. The Orvolle-PF-346 gate often result in crashing into a gate camp getting to the main trunc. Beware there are many areas that are well connected, but there are also some dead-ends you can get camped in.
This is far from an exhaustive list. But if you are looking for a fight, either solo, or in a small gang, these areas are awesome arena's to learn the ropes of PvP and have a good time. Be warned, locals do know what they are doing. Don't fly what you can't afford to loose.