Please provide advice on travel in Australia in July. Will arrive in Sydney July 5 and remain for a conference until July 14 when we are free to travel until departure July 24 (from Sydney). Interested in Darwin area (not Perth or Queensland). Any help about travel from Sydney, good tours, things not to miss would be greatly appreciated!

Aust tower might be a good one to go up and have a look see, but maybe the cloud cover might cut that out.
Keep warm, use the ferry to Manly, train to Bondi Junction & bus to Bondi Beach.
Blue Mountains.
Taronga Zoo.
Manly or Sydney Aquarium.
Lunch at one of the eateries in Chinatown.
Blue or Red bus around the CBD and suburbs close by.
Catch the Kingsford Smith Transit if you are a 1 pax, or taxi if 2 or more.
Train is fast, if you are going to stay nearby to Central Station, but the Kingsford Smith Transit bus takes you on an informal tour of Sydney, I like it. Taxi is fast, but can be quite pricey, depending on what time you arrive, and you also have to pay the surcharges, esp airport pickup (not directly, but that surcharge is indirectly charged).
$2 surcharge, might have gone up due to CPI.

Sydney to Darwin, in the amount of time you have, you might have to fly, taking a hard and fast look at it.
Driving is long, and the train means you have to go via Adelaide.
Qantas will do it for sure, Jetstar I am not sure, have not checked if they now fly to Darwin, Virgin might fly direct or via Adelaide.

Not sure what your interests are but for a short trip to NT, I would vote for Alice Springs/Uluru rather than Darwin. Either hire your own car or campervan or take a tour and do the circuit around from Alice to Uluru to Kings Canyon and then back to Alice. Still quite a lot of driving but not as much as trying to see the sights around Darwin. You can manage it in 5-6 days and you will still have enough time in Sydney for a couple of 1 or 2-day trips (Blue Mtns/Nelson Bay or South Coast) or time to spend a bit longer looking around Sydney.
The cheapest flights will cost about $500 return each - you will need to book soon on the internet to get them at that price.
Have a look at the NT website to get an idea of destinations: here

Hiya, Andy from Sydney here!
You only have about ten days right? Do you get to see anything as part of your conference (sometimes work conferences include day trips to various places). If they don't, then around Sydney my list of 'must see' items would be:
Blue Mountains (absolute must see)
Coogee Beach (and Coogee Beach Hotel for lunch)
General otehr stuff around the city depending on what you are interested in (ie hardbour bridge climb, taronga zoo etc).
I think you should also consider a trip north - if I was you I would be looking to get a cheap frlight to Brisbane and hiring a car - seeing a bit of the coast (perhaps as far south as Byron Bay) - Byron would be a must see on the coast for me as well. Atleast then you have the chance to see Sydney and then some nice coastal places as well!
It all depends on how much money you want to spend and how far you want to travel! Keep in mind that Australia is a big place (its about 7-8 hours in the car from Sydney to Brisbane) so if you are looking to get from one place to another in such a short amount of time then fly and hire at the otehr end!