Both sentences are correct.
It all depends on the situation whether it sounds natural or not.
-となりand ちかく
Maybe you already know the difference :)
となりmeans next to. In this case, the house and the bus stop is next to each other like below.(Hope you can see it as I want...)
○:bus stop
■:my house
□: other houses
----------------------------------
street
------------------------------
□□■○□□□
If bus stop is like this↓ I would say it's "私の家の前にあります(in front of my house)" .
-------------------------------
street
----○---------------------
□□■□□□
ちかくmeans nearby. So it could be in front of or anywhere within 50 meters or so(the number may vary) from the house.
-----○------------○------------
street
--○-----○------------○-----
□□□■□□□□○□□□□□
-がandは
Look at these three sentences. They are all different, and I tried to show the differences in my translation.
1. 私の家はバス停のちかくにあります
"My house is nearby a/the bus stop."
2. バス停のちかくに私の家があります
"Nearby the bus stop, there is my house."
3. 私の家のちかくにバス停があります.
"Nearby my house, there is a bus stop."
(I changed となりtoちかくso we can focus on the grammar here.)
Sentence1 tells where is my house.
Sentence 2 tells what exists nearby the bus stop.
Sentence 3 tells what exists nearby my house.
So, in what situation(s) you can use them?
1 and 3 are common. You tell your friends where your house is, or what you have in your neighbor. 2 is not very common. I actually couldn't think up any situation I'd use it naturally. If it's not "my" house, say, an unknown house painted red(赤い家). Then I can say like this:
"When you come to my house, take bus line 23, get off at xyz bus stop. There is a red house nearby the bus stop(バス停のちかくに赤い家があります). My house is next next to that house."
I think this is why James-san and toru-san above mentions the second sentence doesn't fit well.
But I know it's difficult >< hope it helps!