Different universities are strong for different things. This is what I've heard, but correct me if I'm wrong. Reputation of the faculty is more important for postgrad though: choose a university with a good COURSE for your undergraduate.
Biomedicine - Melbourne University. UniMelb's in the heart of Australia's biomedical reserach precinct, and their medical degree is quite well regarded. From what I've heard, Monash also has a good biochemistry department.
Science - it really depends, but I'd say ANU's the strongest overall. The research areas at ANU are quite specific, but there are quite a few of them and there are brilliant facilities (heavy ion accelerators, solar dishes, telescopes...). Melbourne and Sydney are decent for science as well, but as far as physical/mathematical sciences go, Monash and UNSW are regarded as comparatively weak (although Monash is good for chemistry and UNSW is excellent for engineering).
Engineering - on the whole, I'd say UNSW is the best regarded engineering school.
Below's what I know about courses, which are probably much more important than the reputation of a school in a certain area for undergraduate:
Advanced science courses:
I'm going to write a bit about advanced science courses, because it might be a good idea to consider an advanced undergraduate degree and then postgraduate engineering or something. It gives you more flexibility too.
ANU, USyd, Monash and UNSW offer BSc(Adv). You usually need an ATAR of 95 for these degrees. There are probably other advanced science degrees in Australia, but I only really considered these universities (as well as Melbourne). I think a BSc(Adv) entails studying a certain number of advanced courses or something - I'm doing something a little different. On top of that, USyd offers the TSP (talented students program) to students who score in the top 1% or represent Australia at IPhO/IChO/IMO/IOI/IBO. TSP gives you the opportunity (although it's not compulsory) to do research projects during your undergraduate degree. I've heard both good and bad things about TSP, but it sounds like it's a good program. If you're considering applying to USyd, I'd suggest applying for the faculty scholarships - I got a science merit scholarship (these were given out before ATARs, and merit is the highest non-ATAR scholarship you can get), so if you need someone to read through your application, feel free to ask me. Monash also has a top 1% program called the Dean's Scholars Program or something - I think you get a mentor, and I checked it out with a friend after ATARs came out, but it seemed as though you didn't get to do much research until 3rd year. They're developing their talented students liaison at the moment, and it sounds like it'll be quite good in a few years, but I decided to go to ANU instead.
Here's just a short paragraph on the degree that I'm doing - the PhB (Bachelor of Philosophy) in Science at ANU. It's basically a science degree, but you have a mentor, a lot of course flexibility, and you have to complete at least 6 research projects throughout your 3 years of undergraduate studies, as well as a 4th year of honours. It's pretty cool - my mentor's worked for NASA and other places, and you get a lot of special treatment - yesterday 3 of us went on a tour of the physics facilities at ANU and spoke to the research teams to build connections. You get course flexibility as well - quite a few of us are doing 2nd year subjects this year, and you don't have to have a major so there's also flexibility in that regard. People tend to complain about the PhB kids a bit because we get special treatment - people always seem keen to talk to us, and we have lots of free lunches with professors and things like that. In my year at least, there's a bit of a PhB community and everyone seems to get on well and work together. That said, to stay in the PhB, you need to get a HD average, which means that there's a lot of work involved if you're taking harder subjects.
OK, here's what I know about engineering:
At most universities which offer double degrees, you can combine science and engineering quite easily. I'm not sure if Monash has a co-op program, but I know that UNSW has a prestigious one which is supposed to be quite good. ANU is good for engineering research (I think?) and they have their combined science-engineering R and D program which has a cut off of 99 and you complete research as an undergrad. I don't really know much else about engineering courses though, so someone can probably give you some more advice
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