Doctor Who Experience

Yes, it is easy to travel by bus from the Airport - but where are you coming from? Most people will arrive by train or coach.
Staying in Cardiff at least 1 night as this will give you time to visit the National History Museum of Wales at St. Fagans as well as Caerphilly Castle = a 20 minute train journey to the north & also a Dr. Who location. (Staying in Cardiff will be cheaper than London). (You could combine Caerphilly Castle with Castell Coch by first taking a Stagecoach bus to Tongwynlais) .
http://cadw.wales.gov.uk/daysout/caerphilly-castle/?lang=en
http://cadw.wales.gov.uk/daysout/castell-coch/?lang=en
www.museumwales.ac.uk/stfagans/ (free) (Bus 32 or 320).
Although you can book a through train ticket to Cardiff Bay, the journey is a bit complicated as you must change at Cardiff Central & Cardiff Queen Street & the Bay train station is about 13 minutes walk from Dr.Who. My advice would be to book in advance (for the lowest fares) the train from (wherever) London Paddington (PAD) to Cardiff Central (CDF). Then, when you leave the train at Cardiff Central, go down the stairs but DO NOT follow the herd out through the main north entrance but go the other way in the subway to the south exit .
Then, keeping the railway to your left, walk straight ahead for 2 minutes to the bus stop on the FAR side of the road. Every 10 minutes or so, a number 6 (marked Cardiff Bay or Porth Teigwr) will come. Pay the driver for a return trip - which will be about £3.40 - and the driver will not give change! Get off at Dr.Who. http://www.doctorwhoexperience.com
On leaving Dr.Who, don't get on the bus but walk around the inner harbour passing the Norwegian Church to the Senedd = Welsh Government building. If you wish to see the modern architecture, you can go in for free. Then, head for the Wales Millennium Centre (Opera House), perhaps having a meal first in one of the restaurants on the harbour or in the WMC. (The WMC also has a Tourist Information Centre with free maps).
You could take the ferry out to view the barrage or up river to the Castle (instead of Bus 6). (For day trippers, the bus is the faster option).
Bus stop is by the WMC for the number 6 back to the city centre. Don't get off the bus when it reaches the station but stay on until at least the next stop. If you get off at this stop (Custom House Street), walk towards the modern John Lewis department store and then proceed N up The Hayes. On your right is modern architecture - you might like to walk into the modern shopping mall called St.David's 2. On the other side of The Hayes is Edwardian architecture - you might like to take a peep at the Royal & Morgan Arcades.
Straight ahead are some large trees with a street cafe. Continuing northward, you eventually reach Cardiff Castle and I would suggest that you would only have time for the cheaper self guided tour. If you want the dearer more detailed guided tour, it will take about 1 hour. www.cardiffcastle.com
On leaving the Castle, you may wish to visit The National Museum of Wales (closed Mondays) - which is next to the City Hall. However, if you wish to give this priority, you could stay on the number 6 Bus & ask the driver to tell you the nearest stop to the Museum - most days, it stops practically outside .http://www.museumwales.ac.uk/cardiff/
From the Museum or Castle you can wander back through the city centre shopping area to the Central Station. (Most streets are traffic free).
www.visitcardiff.com
Find trains at www.nationalrail.co.uk but book ahead via https://www.gwr.com (Trains are usually cheaper on Saturdays - providing no major sporting event is taking place). A debit/credit card number is given which can be used at British stations to get your tickets from a machine (chip & pin needed) or a humanoid. If paying on the day, it might be cheaper to buy tickets for separate legs of journey with splits at Swindon & perhaps Didcot -
The train must stop at Didcot & Swindon for this to be valid. 'Details'

I ran past the RS word limit.

All trains on the London to Cardiff route stop at Swindon but not all stop at Didcot. Click ‘details’ on the National Rail website to find out the stops if splitting the tickets.

The Cardiff press have reported that the Dr. Who Experience is going to close in 2017.
http://www.walesonline.co.uk/whats-on/whats-on-news/cardiffs-doctor-who-experience-close-12138399

Thank you so much for all the great information! I will be flying from Dublin into Cardiff on Flybe. Planning on staying just one night. Taking a train into London then for the rest of my trip. The main reason for going to Cardiff is the Dr. Who Experience. I am trying to find a closing date but have not heard back. Your information is fantastic. I so appreciate your taking the time.

The bus from the Airport into Cardiff is the T9 and it runs about every 30 minutes & costs £5 one way. It first goes to Cardiff Bay (stops by the Bay Travelodge (known as Atlantic Wharf) - which is about a 15 minute walk from Dr.Who) - before going on to the central area which is 1 mile to the north. * Route may be subject to change.
https://bustimes.org.uk/services/SMCT009

You may like to consider staying in this Travelodge as you would have the T9 take you directly to the door (*first stop after tunnel) - be sure to tell the driver. Cardiff Bus Number 6 runs from nearby every 10 minutes or so to the City Centre. (No change given - buy a ‘Day to Go Ticket’?) Cardiff Bay rail station is a 3 minute walk to the west. A shuttle train goes from here to Queen Street station in the city centre. From Queen Street, trains run every 20 minutes to Caerphilly - you can buy a through ticket from the guy on the train or from a machine. Note that you need the Central Station for London trains.
https://www.travelodge.co.uk/search_and_book/saver_search.php?search=&action=search&checkInDate=22/02/2017&locpostText=Cardiff&location_code=4574

When is your visit? Are you aware that the Doctor Who Experience is due to close this year? I don't think there's a closure date yet, just "summer 2017."
https://www.google.co.uk/amp/www.walesonline.co.uk/whats-on/whats-on-news/cardiffs-doctor-who-experience-close-12138399.amp?client=safari

I have written to the Doctor Who Experience but no one answers. I think it closes the end of summer-at least I hope so! I just need to buy tickets!

From the local press on 24 January, 2017.
http://www.walesonline.co.uk/news/news-opinion/losing-doctor-who-experience-cardiff-12502445#rlabs=9%20rt$sitewide%20p$17

Thank you so much for the recent Doctor Who Experience closing information! Still hoping it will be open July 5th. Sure is hard for travelers to make plans when no closing date is released. Thanks for the update!!

we've been watching for a closure date quite closely.. the DWE was a highlight of our travel plans.. we're been planning on it since last summer. now it looks like we might miss it. we are hoping to see it the first week of July 2017. fingers crossed

I am also planning on early July. It is hopeful that sometime this month the summer dates will be posted.

I sure wish I could see a filming of Doctor Who even if they were pretending it was another location.
Keep hoping for the best!

We are also planning to visit Cardiff July 18 to see the DWE; fingers crossed it is still open! Any updates on a closing date? How frustrating!

Nothing precise has been stated yet for a closure date - 'July' is the only vague indication made some months ago, but they have remained tight-lipped since.

Its imminent closure has made it more popular.

July dates are open through the 7th.
If you buy tickets, have your payment ready since you will have a limited amount of time to finish the transaction.

I hope all of you get the tickets you want!

Dr. Who Experience in Cardiff closes on 9th September 2017.
http://www.walesonline.co.uk/whats-on/whats-on-news/when-doctor-who-experience-closing-13183111