Yes the areas you are looking at are considered "high density" / "inner city" by some lenders and not by others. If you are borrowing 80% then you should be fine.
If you need to do work to the unit such as renovations then there are two methods you can use to fund this:
1. Use a guarantor loan and borrow over 80% of the property value. When the renovations are complete you can then ask the bank to revalue the unit and if the loan is for less than 80% of the renovated unit value then the guarantee can usually be removed right away. No LMI would be payable. There is no minimum term for the guarantee, you just have to owe less than 80% of the property value.
2. You can get a tender from a licensed builder
to complete the work to your unit. Ideally you should do this right away after a price is agreed for the unit AND ask for an extra two weeks for settlement so that you can get it all organised in the one go. The bank can then lend 80% of the unit value plus cost of construction.