If you had a Pokemon Gym...

Psychic/Fighting, I think. But what about Dragonite?! Oh well, I'll limit myself to two types.
The challenge would be...a mind-bending riddle, with four/five options, and if you got it wrong, you got sent back. There would be a few different riddles, to prompt people to actually DO the puzzle rather than guess every option until you got it right. After that there would be a hallway with two trainers who you can do a double or single battle with.

Battle Girl Sophie:
Medicham
Machoke
Hitmonlee

Psychic Owen:
Kirlia
Riolu
Toxicroak

Then, of course, there's me.
Leader Hayley
Blaziken
Lucario
Gardevoir
Espeon
Gallade

It would probably be the 7th or 8th gym. The badge would be... the Synergy Badge, I guess. :)

Definetly a Dragon type Gym. (points to username) DRAGONS KICK ASS!
I'd probably be the 7th or 8th gym.

Trainers
Each Jr. Trainer has one or two of these
-Bagon
-Shelgon
-Dratini
-Dragonair
-Altaria
-Vibrava

Me- Gym Leader Valkrie
-Salamence
-Dragonite
-Flygon
-Dragonair
-Altaria
-Salamence

And the gym would actually be slightly challenging, with lots of Jr. Trainers and crap.
My badge would be the, uh, Flight Badge? And i would give a choice of 2 TMs, Dragon Calw or Dragon Pulse. I'd take Dragon Claw

A Dark gym, because they rock.
Me:-
A Giratina (i know),Weavile,Shiftry,Absol definitely and I dunno, some others

oh yeah! my sableye, rouge

Shadow type.
Me:
Spoink
Haunter
Missingno
Grumpig
Tyranitar
Umbreon

The type of awesomeness!
Squirtle,Gible...

Err... actually I would have a Dragon/Dark crossover.
Shiftry/Absol/Garchomp/Gible/Weavile/Giratina/Lucario?

Mine would be an optional gym, hidden away in a path off the beaten track. There'd be someone on lookout but if they get given some random item (like a drink. Where'd that come from?) they'll budge and the way in is open.

But yeah, you get in and find yourself in a jungle like maze. This is the gym itself, out in the open. The Pokemon are all varied but everyone has some pretty rare Pokemon - Eevee Evolutions, Safari Zone pokes, out of region etc. And they'd actually be respectable at using them, so think of these trainers are trying to build a half decent team and thinking up of strategies XD

There'd be a few of them dotted about, in a mixture of one on one, double team and continous battles (where you battle one person and another immediately shows up). Until you reach me =D

Straight up, one on one battle. Not sure what team I'd have...either way, I'd have a mixed team. Having one type on your team is asking to get whipped by a few choice Pokemon on an up and coming trainers team. I'll muse on what Pokemon I'd have. They'd be a little strange - if it works I'd bring my Psychic Wigglytuff :3 (But I probably won't).

Of course, EV trained teams would flatten me -_- But instead of a badge that provides nothing towards getting to the Elite Four, I'd give winners a special pass into (another) private area, sort of like the trophy garden - some pretty rares running around for the taking. And some trainers around too, though they'll only battle if you speak to them. The trainers (some of the pokemon) change daily. ^_^

My gym would be a in a snowy area, and I'd pelt any vistors with snowballs. It'd give me an excuse to wear a scarf, and ski googgles, too :D Hmm, my gym would be a secondary gym, since I wouldn't want a bunch of random ten-year-olds bothering me about a silly badge, and if the gym was an actual gym, I'd be yelled at for pelting little kids with snowballs :<

I'd have a maze filled with a bunch of snow traps, and it'd have sleds, too :D There'd be a few trainers, with decent Pokémon around sixty-ish. The trainer would have a neat uniform with blue and cream colors, and fluff :D And when we weren't battling we'd have a bonfire, and a hot apple cider (I don't like chocolate D: ), and hot chocolate. We also go sledding, and a bunch of other enjoyable snow activies. When we get bored of that, we'll start watching a movie or something inside.

Uh, I'd be defeated by any respectable trainer, especially an trainer who uses effort values, against my team of Swinub, Ariados, Houndoom (what, I can't have one D:< ), Venonat/moth, and one of my Fakémon. I'd probably throw a snowball at them as their prize. If a trainer managed to defeat me, they'd be able to visit this one hidden cave place with some awesome Pokémon. If a trainer lost, I'd let them hang out with the gym team :D

I'd have a Gym which doubled as a scientific research building, with various places where pokémon are kept, labs and other such, but they're not important. You do, however, need to find me, before we go to the battle arena.
My team would, for the first battle, consist of:
Eevee
Vaporeon
Jolteon
Flareon
Leafeon
Glaceon

later on you can challenge me again, at which point I will use a random set of pokémon, which is very variable, and will often focus on a 'theme' such as say reptiles.
I also appear in other places, doing scientific stuff, and I have different teams, but including pokémon with the games HM moves (yes even the useless one).

Also maybe I'll fight with the player at some point in the game.