Depending on the runways in use, there are several locations. I can offer a number of suggestions, but you need to consider a few things. I was there last week - it was stinking hot. The sun is very high in the sky now. Heat haze and a sand-storm giving seriously crappy conditions. I'm certainly not telling you to not bother, but without a car you'll be seriously exposed. That's not an issue in the winter, but in June you will need to be very careful. Check www.suncalc.net
to see the sun position at this time of year. It's not wonderfully conducive.
In terms of the police, yes, if seen you will almost certainly be taken to the police station for a LONG talk. You may also be asked to sign a document (in Arabic) which I believe states that you "won't do it again". I've lived and worked in Dubai and, touch wood, have never had an issue. However, plenty of people I know have been interviewed by the police and eventually released (after several hours). I don't know anyone who's had equipment or cards/film confiscated.
In summer it's not unusual for them to be on 30s all day long. If they are, my recommendation would be to try shooting departures in the morning, then move the the east end in the afternoon to shoot approaches. Nearly all departures will be from 30L. You'll need to be north of the runway until around 11am, between 11 and 12 the sun is almost straight down the runway. After about 12:30 you could move to the south side.
None of these locations is great without a car
Early am until about 11 : N25.272 E55.348 (car park, two metro stations within a short walk - Abu Hail & Al Qiyadah)
Early pm until about 2 : N25.262 E55.336 (small park with some trees for cover)
Early to mid afternoon, go to the east side for approach shots.
Somewhere in the area of N25.222 E55.408 BUT, this area is very exposed. You can take a taxi to Carrefour in Mirdiff and take a short walk. There is no cover here whatsoever, so not only are you exposed to the elements, but you'll be rather obvious.
I really think it's hard without a car, especially in summer. If you do go for it, take care and be as discreet as you can. Good luck.
Time flies like an arrow. Fruit flies like a banana!