I don't know where to live

The rule of thumb is that if you go towards the more modern part of Dubai i.e. downtown onward, the apartment and neighborhoods are much much nicer but then again, the rents are also extremely high compared vs. Deira / Bur Dubai.

DIFC/Downtown is expensive.  As a compromise, you could look at business bay which is right next to these areas and has tons of apartments where you will find better value. Business Bay also has metro stations and is on main SZR.   If you are open to going much further, you can find affordable options in TECOM and JLT (Jumierah Lake Towers) but that might be too far. Again, these places have metro connectivity and are on main SZR. I would skip Barsha as for me, it just comes across as a slightly more refined Deira.

Also when you say "in the city", keep in mind that for Dubai old timers, Deira/Bur Dubai IS the city as these were the only populated places a few decades ago and everything else was desert.  They see the rest of Dubai as a new development to which they will resist moving to.

Thanks for the reply!

Yes, I heard that about Deira! I like it, it's very convenient but the good apartments I found are also around 60K so I'd rather spend that closer to Downtown.

I heard traffic from Business Bay is really bad? It's over an hour and a half on public transport now but I think I could do some of that journey via taxi and hopefully be driving in a few months

Rush hour traffic going from Dubai to Sharjah is horrendous.  And you will face the worst of it. 

And yes, getting in and out of business bay at peak times is bad.  The exit is a relatively small one and it is clogged with long lines.

Essentially, you need to get a car and then your options really open up.

Hmmm.. I might be better off staying where I am until I get a car in that case?

Yes

Is it normal to spend half your salary on rent here??

No.  And it never is.  At max, you should spend 33% of your salary on rent.

yeah I've been trying to stick to 48,000aed max but I haven't had any luck

In the good areas, that unfortunately won't even get you a studio.  You probably need to manage your expectations or be ok with spending 50% - which I personally think is unnecessary.