The easiest place to put the relay is in the engine bay, in the front corner somewhere, you will be able to intercept a high beam wire close by and you won't have a long cable run to either the lights or battery.
Just an on/off mini relay will do, but see if you can get one with an integrated fuse.
I'd also take the opportunity to run the high beam through the relay while I was at it.
Doing so will probably make your lights brighter, bulbs last longer and take a current load off your under-rated headlight switch, for these reasons, I'd fit another relay to the low beams as well.
In fact, I'd go for a New Era duel relay (part # NLR-132) these are quality units made in Japan and have integrated fuses. using one of these will simplify the wiring as to do both high and low beams you'll only need 1 earth and 1 power feed.
Easy to wire up;
Battery feed to B
Earth from S
Switch low beam to S1
Switch high beam to S2
Low beam light from L1
High beam light from L2
If you can't find one of those then go for a relay with a high amp rating @ 30 to 40 amps or so should do.
As for where to put them, somewhere under the bumper, that's where I found space for both driving and fog lights.
I'd show some pix of the car, but it's too much buggerising around since Photobucket (Pissbucket would be more like it) decided to become totally avaricious arseholes and stuff up the internet.
Has natural justice been done, and that bunch of rancid turd-burglars at Spewbucket gone broke yet? I hope the bastards all get pizzle rot and their tiny dicks drop off! (Mind you, who'd notice?)
"Keep calm, relax, take a deep breath, focus on the problem & PULL THE BLOODY TRIGGER"
'80 Triumph TR7.
'97 Ford Falcon Longreach 'S' ute,
'98 MG-F.
'83 Jaguar XJ6 Sovereign S3.