Heathrow to Drury Lane in Holborn
 

I will be arriving at Heathrow early in the morning 7Am on a weekday and wondered if it is workable to take the tube with a large suitcase at this typical commuter time in the morning.
In addition I will be departing later in the week from Stanasted and was thinking about taking the train to the airport. Any advice about either trip would be appreciated.

you might want to take the heathrow express(train) to central london and then the tube to holborn- this will be much faster and easier. Again for stanstead , take the express, takes 15-20 minutes as opposed to taxis which takes 1 hr or so and costs £40.
you might want to check national express coaches, which takes you to several points in london.

Drury Lane's in Covent Garden. Most places in it are are equidistant between Covent Garden tube and Holborn tube.

Wit the greatest possible respect to Chinmum, getting the HEX is utterly dozy. It costs about the same as a transatlantic flight, and you've either got a lengthy queue for a cab at 0830-0900, or a really ghastly tube journey: you're dragging your case onto 2 tibe trains (no direct connection), both chocker.

Get on the tube at LHR, where it'll be relatively empty. You'll have a seat into town and the tube goes straight to either of your tube stations.

For Stansted, there are a range of choices at the "getting here" section of the Stansted website. The train is fastest (though getting to Liverpool St or Tottenham Hale stations isn't that easy), National Express cheapest and possibly the Snowdrop Travel A60 from nearbyish Russell Square the most convenient for where you are

flanneruk is absolutely right; it would be barking mad to get the HEX. To be honest, yes, it might be slightly uncomfortable on the tube at this time but Heathrow is the start of the line so just get a seat and put your bag somewhere sensible and watch it get busier! It will take probably 45 minutes or more on the tube but you don't have to change so it's the best option.

In case you haven't been convinced yet -- The Heathrow Express is about the WORST option for you. The tube from Paddington to Covent Garden would require a line change -- most likely at Piccadilly Circus which can be a total zoo.

However don't assume Covent garden is the station you want. Drury Lane is fairly long. The southeast end is near Covent Garden station and the NW end is near Holborn station.

So if you give us the actual address we can help more (the travel advice would not change whichever end of Drury Lane you are on)