Hi Laura,
I have also stayed at Travelodge Wynyard. As has been said, at the prices you pay, it is well situated and the rooms are reasonable. You will be only a short walk away from The Rocks, and therefore the Bridge, the Opera House and the Botanical Gardens. You are also close to Darling Harbour. My wife and I walked as far as Chinatown one day, and came back by monorail.
If you are feeling adventurous, do the Bridge climb while you are there. It is not remotely strenuous, hard as that may be to believe. Also, you might enjoy the ferry over to Manly, where the beach is beautiful. The ferry takes you out past the Opera House and it is really a very nice trip.
You can also take a circular route bus to Bondi Beach if you prefer, though I thought Manly was nicer. On the bus trip, you can get on and off the bus a often as you like, so you can visit Bondi and several other places in one day.
One thing I should mention about Travelodge Wynyard. I booked it for seven nights and chose it because we were going to stay up in the Blue Mountains for two nights in the middle of the trip, so I wasn't paying for 7 nights in an expensive hotel and only using 5 of them.
On the day I left, they handed me a bill for drinks from the minibar and use of the internet from my room. We had no drinks whatsoever from the minibar, and I had used the coin-fed internet machine in the reception lounge area for internet access.
I argued this with the girl at the desk and she relented and reluctantly scratched the bill. However, I'm sure she thought I was lying. I was convinced that this bill must have been rung up during our two night stay away in Bilpin Springs, but did not have the time to check this, as my transport to the airport was waiting.
Might have been a one-off, but you never know.