Late night flight into Stockholm, transportation into city?

The last departure of the Arlanda Express is at 1:05 am, so you should have time to make that. It will take you to the Central Station. Thursday to Sunday, you can get a discounted ticket cor two persons. The time table is here:
https://www.arlandaexpress.com/mandagfredag.aspx
You'd then have to travel to your hotel. If you tell me where it is, I can help with options.

Alternatively, you can take a taxi for a fixed price (around 520 SEK). However, taxis are unregulated so it is very important to use one of the reliable companies ... either Taxi Stockholm, Taxi Kurir, or Taxi 020. i usually use Taxi Stockholm and you can prebook from their website.

Thank you, Laura!

The hotel's address is Riddarholmen, 111 28, STOCKHOLM (hotel website: http://malardrottningen.se/home.aspx)

Based on this taxi's website, it might be best to book a taxi -- the Arlanda Express would be 1060 SEK total, whereas the taxi looks like it'd be 500 SEK per hour. I hope I'm reading that right (http://www.taxistockholm.se/en/Fare-and-payment/)

CORRECTION. I just noticed that you arrive on a Wednesday. The price would then be 280 SEK each (560 SEK for 2) since the discount is only Thurs to Sun
https://www.arlandaexpress.com/fares.aspx

I'd take a taxi and ask for a fixed price at that time of night.

I forgot to ask which airport you are coming into. I assumed it was Arlanda. If it is Skavsta, then things are different.

Also, this is the rate you want --- the fixed price from the airport:
http://www.taxistockholm.se/en/Taxi-Stockholm-Services/Arlanda/

you can also just go to the taxi queue and look for a taxi from one of the three companies that I mentioned. Ask the price.

I'm so sorry for responding so late, Laura! This has been hugely helpful. I truly appreciate it!! :)

Is the subway system pretty simple to use? Im going to stockholm in June and am a bit anxious....

The subway ("tunnelbana") and bus are very simple to use. Many signs are in both Swedish and English.