Stay in North Greenwich???

Could you give us more detail about the location? Twenty minutes by bus from North Greenwich could be an okay area or could be really not - it covers a lot of ground!

My first impression is that North Greenwich tube itself is a bit out of central London - I wouldn't recommend it as a location for a first-timer - and I certainly wouldn't want to travel 20 minutes by bus to a tube station then another 20 minutes or so into central London.

It doesn't sound that convenient - the journey might get increasingly tedious as you do it time after time. Advice might be more useful to you though if you say where you are actually considering staying. Twenty minutes by bus covers a fair area.

ctlambeth, North Greenwich tube station is in the middle of an industrial area which has had a lot of "regeneration". 20 minutes from there by bus would be in any number of residential areas of London. Not inner London, but not up-market outer suburbs either, just where millions live and commute from. The whole area also has a dense surface commuter rail network which, depending on where in central London you are going to, may provide a faster connection.

This is well within the London boundary, and totally built up I would not expect to find anything I would call a "cottage" in this area.
But, as this is where normal working people who commute daily to central London live, travel is no problem.

Can you give us a link to your rental, so we can see the exact location please?
Is it a rental from AirBnB or VRBO?

Here is a link to the property: https://www.tripadvisor.com/VacationRentalReview-g186338-d4567919-Enchanting_Victorian_Cottage-London_England.html

That is no "cottage", there is one outside view shown ( https://media-cdn.tripadvisor.com/media/vr-splice-j/00/fa/e0/af.jpg ), which is a rear view and it looks like a normal Victorian or early 20th century end terrace suburban house. Nothing wrong with that.
To me, a "cottage" is a free standing rural house in or outside a village, not a suburban house; but they have to sell the place, so a certain amount of b---sh-t is to be expected.
Looking at the map, the nearest station is Eltham, about 1½ Km away, or 20-30 minutes walk, but there may well be a bus to the station. Lots of services into central London (click here), taking 30-40 minutes. North Greenwich is a long way further.

From what I can see, nothing against the place. If you want to stay outside central London (but still well within London), sacrificing travel time for price, go for it.

"This is our first trip to London" you said.
I think this is a mistake, for you to stay this far out for your first trip to London. Just my opinion.
You need to stay in a central location in London, so that you can walk to some attractions and take a short tube or bus ride to others.
If you are looking for an apartment, you need to keep looking.
Look in the neighborhoods of central London.
If you would be happy with a hotel, say so, and we can provide some suggestions.

It's much easier to see several sights a day if you are close to a couple of them when you wake up in the morning.
On their first trip to London, most people pack their days with sightseeing.
You will see more per day staying in central London.

I would certainly not stay that far out of London. From Eltham station you'll be taking suburban trains which, if you are travelling into central London in the morning and out in the evening, will be absolutely packed. That's also too far from the station itself than I'd want, so you'd waste even more time travelling.

I found it on Google streetview: https://www.google.ch/maps/@51.4703813,0.0599641,3a,47.6y,38.23h,90.15t/data=!3m6!1e1!3m4!1sZpPf5fTSD9zY2kJEN4njng!2e0!7i13312!8i6656!6m1!1e1?hl=en
Compare the above with the rear view on the Trip Advisor site ( https://media-cdn.tripadvisor.com/media/vr-splice-j/00/fa/e0/af.jpg ), definately the same building.

I would describe it as a late Victorian brick built end-terrace. Between a pub called the "Red Lion" and a convenience store, on a road called Shooters Hill, Woolwich, which is the old road from London to Canterbury and Dover, but has now been superseeded.

I even found the pub website: http://www.theredlionwoolwich.co.uk/index

I'm thinking this could be a noisy location, with the Red Lion Pub on the left side of the rental, and the Premier Convenience store on the right side. Could be lots of people drinking at the pub until late at night.
The Red Lion website (that Chris furnished a link to) says they have a large beer garden in the back that is open in the summer.
There would possibly be cars coming and going from the parking lot of the pub, and from the convenience store (open all night?).
From looking at the Google street view, there is a lot of traffic on Shooters Hill Road.

It will be noisy there.
And especially if you stay in the summer and need to open the windows for some air.
Then you'd never have a peaceful nights' sleep.

No, I do not think this is reasonable or feasible.
I assume you have continued to look online.
What other apartment rentals have you found?

Have you looked into commuting by water taxi? Shooter Road doesn't look that far from Canary Wharf if there is a taxi wharf near you on your side of the river.

"Have you looked into commuting by water taxi? Shooter Road doesn't look that far from Canary Wharf if there is a taxi wharf near you on your side of the river."

Kathleen, great idea! That pier is Greenwich Pier. I was also thinking of that as a travel option for the OP.
Ctlambeth would walk down Shooters Hill Road, enter the park, walk past the Greenwich Royal Observatory, continue on down the hill on The Avenue, which turns into King William Walk. You will begin to see the tall masts of the Cutty Sark ship; continue walking toward the masts.
You will eventually come to the waterfront, where you will board a boat at the Greenwich Pier.
It will possibly be a Thames Clipper boat.

As you travel by water toward London, you will see Canary Wharf (clearly labeled--there is a large sign on the end of the dock) on the north side of the river. It is some distance away after you leave Greenwich.

This is probably the most enjoyable way for you to travel into London, if you decide to stay at this rental.

The only drawback is that if you return this way, the walk from the waterfront of Greenwich up to Greenwich Royal Observatory is quite a long, steep walk up the hill. What a hill!! We almost gave up before we got up to the Observatory when we were there in May 2016!!

Everyone thanks so much for your advice! We are looking for a flat closer to the center of London.