If there is a stud back behind the wall, cut a piece of wood to fit in the hole, nail it with a couple nails, and use drywall mud to fill smooth---and then as it is almost dry, you can texture it kinda like the wall.

Or, use the base molding ---with a 45 degree miter to cover the hole. You could put a return cap on the top end.

You could make your own block to fit here. I had a similar situation and I made the block from a poplar board that I bought at Carter Lumber. This is yellow poplar---it is easily worked. I would make the block wide and very bold so that it makes a statement and doesn't look like you're trying to cover up something. You could rout a radius on it, or because it's so easy to work, you could sand a radius edge on it. You could do a carving in it--that's what I did. Or, glue on a fancy applique that many of the bigbox stores carry. I would bring it all the way to the floor and butt your baseboard against it. You could take it all the way up to meet the stair stringer and it would look all united.

I think the correct way would be to cut out a square of the sheetrock and patch with a new piece that butts up to the stair stringer. Tape and replaster.
Another easier option would be a piece of 1x2 cut long enough to cover. Paint it as the risers are and butt the baseboard against it. Round off the top of the 1x2 to match the profile of the baseboard.

I think you should put a piece of vertical molding there that matches the baseboard molding and miter them at 45 degrees where they meet. It will cover the gap and look much more finished than a drywall repair. You can put a little cap at the top to terminate it nicely at the second step. Consider it a plus: you need something there to dress up that plain corner.

Thanks for all of the suggestons. I was thinking of doing what kudzu9 suggested, but didn't know if it would look weird having baseboard molding that comes out in three directons from the same corner..(left, right along the floor then vertical). I think when we start putting in the molding we'll sit some pieces in place and see what it looks like. If it's a bit much, we may go with the 1x2 piece as beacher003 suggested. I'm not sure if I can patch the hole as there is nothing back there to attach a piece of drywall to, but may reconsider that if I think I can figure out what to put back there to attach the drywall to, and also if I feel I can blend in the plaster there.

Thanks again. I'll keep you posted.

Quick drying liquid nails is great to attach nailers in hard-to-reach areas.
You can glue the wood to the existing stud and then patch w/drywall if you don't like the look of trim.

Just a comment, and hey, this is my asthetic, and not necessarily anyone else's, but it looks a bit odd to me with the end of the trim running down the side of the stairs visible like that. To me it looks like something that needs finishing, and I'd do it with trim coming up from the floor that would cover the hole.

Hope we get to see pics of the finished product!

I think the plan is to run the baseboard up the wall. Whether or not we meet the other trim will be determined on how well we can notch out the carpeted step in our way. The new baseboard we're putting down won't match the older baseboard running down the stairs so we didn't know whether we should try to bring one up to the other or not...I will post pics when finished...I just don't think anything will really look right. We may try to repair it...and cover it up with baseboard if it doesn't turn out right! I'll post photos when done!

Baseboard will look strange here. I was the one who suggested you make a block for this area. But here is another idea that will look very good. You could use some full profile door casing. By full profile, I mean the kind of case that's used with corner blocks because it is a full 3/4" on both sides----not tapered. Some of it has flutes or beading that would look nice and some of it is 5" wide. I would use something wider than your baseboard.

Here is something else for you to look at----it might give you some good ideas. This website is one I found a while back for corbels, but they also have some neat wood panels that you might find useful. It's under "new products" on their site. www.osbornewood.com

I forgot to tell you about Power Grab. It's an adhesive used for moldings, wainscoating,etc. It's used where it's impossible to nail molding. It doesn't need clamping and is a better product than liquid nails. I've used it extensively and it works very well. If you use a wide enough panel to cover this gap,you wouldn't even need to repair the hole. But if you need the hole repaired, you could put some fiberglass screen over it and bondo it.

Thanks for the suggestions...green-zeus I am familiar with Power Grab. We bought some a few weeks ago for some reason (think I saw and ad and just wanted it) so I will put it to use. I will check out the full profile door casing...

I will consider gertie's thought about the top part looking unfinished...not sure how to address that part now!

I've put this off for awhile, but need to get on it again.

Thanks!

The area where the trim board ends is definitely a concern. It might just be an illusion in that picture, but it looks like only that top tread overhangs and the others are flush with the stringer. If you could trim that overhang, it would help with your installation. It would be good if you could install the panel up to the top of that trim panel,too. And maybe you could leave a 1/4" reveal between it and the decorative panel to give it a professional installation look.

It looks like a trim piece that is flat & wide (3/8" x 3" wide by 20" or so long) enough to cover this gap & paint it white to blend in!

It's really too bad they didn't make the treads & risers wider as the stair comes down below the wall, like 3-1/2" wider because that would have given you an area to set your balusters on the treads as the rail ran up the stair & stopped at the wall. Hind-sight, don't you just love it! Old Stair Guy