Post a concept plan of your kitchen and you'll get more specific feedback.

First thing to think about is what else can you use that peninsula for?

If there is a cooktop on there, it will mainly be cooking/prep.
Pots, pans, heat, mess, will keep you from setting much else down.
Ventilation will be: none, hood hanging overhead in mid-room, or downdraft.
Downdrafts do not work as well. A hanging hood will be a large visual item.

If cooktop is elsewhere, peninsula can be used for prep, baking, buffet serving, gift wrapping,
Flower arranging, homework, craft projects, spreading out the newspaper, etc.
Hood options against wall/under cabinet are more varied, type and price wise.

Peninsula Cooktop No Hood

Peninsula Cooktop No Hood (possible downdraft?)

Peninsula Cooktop and Downdraft

Peninsula Cooktop with Hanging Hood

Here is another idea...How about putting the range on the sink wall?

White Kit Peninsula with Range on side wall

Wood Kit Peninsula with Range on side wall

Mod Kit Peninsula with Range on side wall

My preference is to keep the peninsula free for multiple uses.

Ivory U-shaped kit range on far wall

Dark Wood U-shaped kit range on far wall

Small Ivory u-shaped kit range on far wall

Good Luck!

My peninsula isn't very long either and I put my microwave under the counter in that spot with a drawer underneath. I didn't want my MW being seen and it it hidden, but useful, in that spot.

True, you can put a MW down there instead of a range.

Bad pic showing MW on shelf under peninsula.

We did the same as blfenton with the microdrawer - and I have loved it. I have a bread drawer under the micro (and toaster to the left) so lots of sandwiches are made there, it is super convenient.

Even though there are a lot of reasons NOT to put a cooktop or range in a peninsula, it really depends on the overall kitchen layout. It just might end up being the best place for it. In every kitchen compromises are made. So while in MOST kitchens, the cooktop should not be placed on the peninsula, there is no way to say for sure without looking at the OP's kitchen space.

I have a small kitchen with a peninsula between the kitchen and dining room. I use it for many of the uses biochem101 stated. One cabinet faces the dining room and holds holiday dishes and tablecloths, the other cabinet faces the Kitchen and holds pots and pans.

Dining Room side:

Kitchen side:

I like the MW over the stove...it not only vents, but leaves the peninsula for other activities...i.e. eating bar, homework, etc.

Thank you all, most especially biochem101, really amazingly helpful and thought provoking. I will post a layout as soon as possible, mahalo from Aiea, Hawaii.

Can't wait to see what you decide on - I'm in the design process myself and have the same question! Thanks everyone for the inspiration without asking yet.
I've been thinking of putting my microwave under the counter and possibly in the peninsula...as if you need more ideas ;) had to share these:
http://www.houzz.com/photos/query/kitchen%20island%20microwave

I have a peninsula and given the room dimensions, the peninsula was the best choice for the stove.

I did go with a hood very similar to the glass hood pictured above and we just had it put in. Really like it. Whatever you decide on stove location, I would get a decent hood--it is night and day over the junker we had before. My friend with a downdraft says it is so useless she doesn't bother anymore. (Note that an island or peninsula hood costs more as it has the tube has to be finished on all four sides.)

biochem101... where did you get the photo I linked below, the peninsula with the post?

Here is a link that might be useful: