The 802.11n standard provides mechanisms for operation in either the 2.4GHz or the 5GHz band, but it does not require that any equipment supports both. Some 802.11n gear is 2.4GHz only, and some gear supports both bands. I'm not sure I've ever seen any 5GHz-only 802.11n gear, but I wouldn't be terribly surprised if it exists.
Some APs that support both bands only have a single radio set, so can only be configured for one band or the other at any given time. Other APs have dual radio sets so they can support clients the 2.4GHz band at the same time as supporting clients in the 5GHz band. The 802.11n standard does not specify a way for a single client adaptor to use both bands at the same time while talking to the AP.
Connecting legacy a/b/g gear to your 802.11n AP does NOT bring the whole network down to legacy speeds. That is a huge myth or lie.
Packets to/from the N clients go at N speeds (assuming the N clients are at close enough range to use N), and packets to/from the legacy clients go at legacy speeds. Beware, however, that the legacy clients require more airtime to send the same amount of data. So it can take an 802.11g client more than 8x as long to send a certain sized packet as it would take a modern 3-stream HT40 N client (54 vs 450 mbps).
Using that example, the modern N client, if it had the airtime all to itself, could download a 27 MebiByte file in about a second (this is assuming total Wi-Fi + TCP/IP overhead of about 50%). But the legacy G client, even if it had the airtime all to itself, would take over 8 seconds to download that file.
Now let's say both clients are on the network at the same time, and both start downloading the same-sized 27MiB file at the exact same time. And let's say they share the airtime roughly equally*. The modern N client will now take 2 seconds to download the file, and the G client will take 9 seconds. The G client only gets half the airtime the first 2 seconds which it's competing with the N client, so it only downloads 1/8th of the file, instead of 1/4 of the file, over those 2 seconds. But then after 2 seconds, the N client is off the air, and the G client gets all the airtime to itself, to it's able to download the remaining 7/8ths of the file in 7 seconds.
That was a simplified example, but it gets the point across. For the sake of completeness I should add that there are some minor performance optimizations that N gear can do when no legacy gear is around, but losing those minor optimization is a small impact. It's nowhere near the "it drops the whole network to legacy speeds" myth.
If you have an AP capable of simultaneous dual-band operation, enabling both bands at the same time is about the same as having two separate single-band APs, one in 2.4GHz and one in 5GHz. Both instances are able to use just as much power as they'd always use. And assuming you buy a high-quality simultaneous dual-band AP, it should have enough CPU horsepower to move packets at full "line rate" on both wireless interfaces, and its wired Ethernet interfaces, all at the same time.
*In actuality, the G client and the N client probably wouldn't share the air time equally; the N client would probably get significantly more airtime. This is because 802.11n allows frame aggregation, which allows N clients to stay on the air for longer blocks of time, sending multiple frames per each "turn" it gets on the air. Some G clients did something called frame bursting which wasn't really part of the 802.11g spec, but had a similar effect. So a framebursting G client vs. an aggregating N client might share the airtime roughly equally.
Update: One last note: The minor slowdowns caused by legacy radios would be caused by any legacy radios on the same channels, or nearby on overlapping channels. They don't have to be APs (routers), and they don't have to be clients. They don't even have to be on your network at all. It's just a matter of being visible on the same channel or an overlapping channel. So if you had all N gear in your apartment, and your N network was on channel 1, and your next-door neighbor also had a different network on channel 1, and your next-door neighbor had one more more legacy clients, that would affect your performance almost as much as if you had a legacy client on your own network. But again, it's not like the whole network drops to legacy rates.