Cabinet above the stove would go against building Code. Cannot do that. You cannot have anything combustible directly above the stove like cabinets. I suggest you buy an inexpensive hood from Costco that has a recirculating option, i.e. it doesn't vent to the outside.

BTW, some condo buildings do have exhaust to the outside, while many don't. If you are buying a condo, I would ask this question before purchasing.

If ventilation and good indoor air quality is important to you, don't buy a condo.

What kind of response is that?

What about a shorter cabinet with a recirculating hood?

Nosoccermom - I already suggested the recirculating hood. Don't know what you mean by shorter cabinet. OP can get a hood that is 9" tall which should fit fine with an existing cabinet that previously had an OTR MW hanging from it, while allowing the appropriate 30" distance bet cooktop and bottom of hood

The most annoying thing about an under-cabinet recirc hood is that the only recirculating hood that really does much is the Vent-a-Hood ARS system and they don't make one in that configuration.

If you can afford to lose the cabinet above the current microhood, that would be your best bet, but they only come in a chimney hood wall mount style. See:

http://ths.gardenweb.com/discussions/2347276/vent-a-hood-ductless-ars-range-hood-update?n=61

With that VAH recommendation, we'd need to know the budget. From what the OP said (asking about having no hood at all) I get the impression that ventilation is not that important to him/her. VAH is $$$

A recirculating hood of some sort is needed but it doesn't have to be part of a microwave. You can replace the microwave/recirculating hood combo with just a recirculating hood. I just searched on the AJ Madison website and there are 669 ductless hoods available in many styles and sizes. I'm sure one could meet your needs. Yes, having a ducted hood would be preferable in a perfect world but if the buildings you want to buy in don't offer that you'll have to make a decision on how important a ducted hood is to you.

https://www.ajmadison.com/b.php/Non+Ducted%3BRange+Hoods/N~32+1178

With that VAH recommendation, we'd need to know the budget.

Well, yes, it is much more expensive. But if not that one, it doesn't seem to matter much which one these days--the rest are pretty similar to each other in performance or lack thereof.

That's why I advised OP in my first post above to buy recirculating hood at Costco

Thank you for all of the replies. I don't really care about circulating air. I don't cook anything that smelly. I can open a window. I just want to like the way it all looks. I guess I can disguise the recirculating hood. I find them all very ugly. THANK YOU AGAIN.

My "what kind of answer is that?" was directed at Sophie Wheeler's comment about living in a condo.

To m miller, I misunderstood your statement that you can't have a cabinet above a stove. You meant a cabinet without a hood below it?

Code requires 30" between cooktop and just a cabinet above or 24" if you have a hood or insulating material.

I like that recirculating slide out hood--it's isn't obtrusive at all.

But not cheap, either, unfortunately.

Alternatively, IKEA built-in hood. 399.00.

https://www.costco.com/Ancona-B428-28%22-Built-In-Range-Hood--AN-1305.product.100291752.html