I've visited both cities plenty of times, and as a tall Aussie strolling the streets I've never had any real issues. That being said, I'd definitely list Kuala Lumpur as my preference as the better city to visit as a tourist. It's easier to get around with public transport (though the new busway in Jakarta isn't too shabby so long as you're staying near one of the stops).

KL probably has more sights worth seeing too, though both only probably have a few days worth of tourist attractions overall. That being said, if you had a week in the region it's easy enough to do both cities and experience the best they have to offer.

For Jakarta, the best hotel is probably The Dharmawanga - http://www.the-dharmawangsa.com/ - it should just squeeze in your budget range. Otherwise there's all the usual high-end brand names (Four Seasons, Ritz Carlon, Hyatt, InterContinental, Mandarin Oriental, etc etc) though none of them are the best of their respective brands, also at the high end there's the Hotel Mulia http://www.hotelmulia.com. You can usually get some very nice weekend rates at most of these hotels though.