Probably hostas.

Does rain runoff escape via the back lot line or the front? (I'm asking about overall lay of land.) And which side of the house are we looking at?

We need a picture where you backup a little and line the camera location with the window but aim to the overall center of scene.

Also, how do you want to use this space? Will it be a sitting area, a wildlife garden, low maintenance shrubs/perennials, etc...

I agree some more info for sure

@Yardvaark @cecily7A thanks for the response, i will upload few more pictures asap. Rain water usually run off there is a path created by the builders landscaper but if there is continuous rain then it takes lot of time for this part of the land to dry compare to other. This is back side of the house just behind the Car garage. Right now i am looking for any sort of suggestion, wether its a landscape or hardscape which ever can help make this land live again.

It takes time to dry because the area is quite shaded :-) And for that reason, I'm not sure a hardscaped seating area is an appropriate use (also because it is tucked away and does not look readily accessible). I'd just make it into a shade garden with hostas, ferns and other shade loving plants that appreciate moist soil. Not knowing your location, can't make specific plant suggestions but there are scores of great looking shade plants to choose from!

Hostas, but you're not going to get any exotic varieties at the local big box store. Watch for yard hostas sales in your community or go to a private nursery for your best selection

OP, you forgot to say overall direction of drainage.

For a moist area next to the house, I would want to check to make sure the moisture is not damaging the house in any way, and fix any drainage/slope issues first. Moisture intrusion can wreak havoc on a house.

Once you know that’s okay, this doesn’t strike me as an area where you’d naturally want to hang out or have a patio on, so I agree with others to create a planting bed and plant a variety of shade-loving, moisture-loving plants. A local nursery can direct you to what plants will work well on your area.

@DH it would not hurt to get it checked by a professional about the moist condition and if it is effecting the house in any way. Who can i contact for such kind of services?

Definitely get the drainage problem checked out before you make any other decisions. Or it could be long term problems for your foundation and a future wet basement. For starters your 2 downspouts need extenders on their ends so rain runoff is directed away from that area. The splash blocks you currently have don't extend far enough (FYI, one of them is backwards). If you are going to use this area for living space you might want to have an underground runoff system. It can be a DIY job but their are companies that will install. Google basement waterproofing for companies in your area.

Ask around and search for recommended drainage specialists in your area. Yelp, Angie’s List, and other such sites can be helpful if needed, just do your due diligence like you would with any other contractor.

There are are things that you can check yourself, to start assessing if there’s a moisture problem. Here’s an article that goes into that somewhat.

https://www.houselogic.com/organize-maintain/home-maintenance-tips/drainage-problem-signs/

@Yardvaark here is the new picture as requested. @Dig Doug's Designs i really like the design. If i have to start the ground work then who can help me with the inspection or who should i reach out to have them inspect or take a look at the damp condition.

Check with drainage specialists in your area.

Just wanted to add that drainage might well be a non-issue :-) Is there any indication of leakage in the basement or crawl space adjacent to ths area?

Shady, enclosed or protected areas are very slow to dry out after a rain as there is little direct sun to help with evaporation. This very common in many shady areas and has nothing to do with improper drainage.

Fill the corner with pebbles and add a bench. You won’t sit there, but it will look comfortable and inviting. The rocks allow the water to drain.

If planting, please look into native plants in your area. Many of them thrive in wet shade. Some bloom vigorously.

@Amit ... the "new picture" did not appear. You must wait for image to go from greyed to full color before submitting.

@Yardvaark here is the image again

Amit, I'm asking for the third time, does the overall drainage go toward the front or to the back of the property?

It also looks as if the ground is very uneven, so there may be puddles that take awhile to dry out.

The ground should slope evenly away from the house towards the property line, and from there drain either towards the front or back of the property.

The downspouts should have extensions so that the water exits at least 6 feet away from the house.

Yardvaark sorry about that. So the backyard has slope and the drainage go towards the back of the property.

Here are some things you can do, called out on the drawing.

Since you need to fill in a dip and make the slope drainage away from the house uniform, and you need to increase the capacity of the gentle swale, you can use the soil you dig from the swale to fill in the dip. (We can't see the path of the swale. It needs to be ever-descending until it blends into sufficient slope in order to carry the water away. The swale should blend gradually to the surrounding grade -- not be like a trough or trench.)

One of your splash blocks is on backwards. The other is not positioned to catch water.

You can purchase a downspout tailpiece to turn sideways as I'm showing in red.

After you fix grading and drainage, you can plant with a couple of shrubs and fill with groundcover so as not to mow in this niche.

@Yardvaark thankyou very much for the a practical suggestion. Can a landscaper help me with the drainage and grading issues or i need to look for some other professionals ?

A landscaper should be able to help you if there's nothing more major than what we see in the picture. I cannot see the grade of the entire "swale" so don't know what you might need to scrape out in order to make sure that escaping water is not blocked.