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If the Online ArcGIS server is not available (no subscription), you can create a DEM for a larger area by downloading small areas of DEM from the National Map Viewer website and mosaicking them together and reprojecting to the desired coordinate system.
Download DEM data from National Map Viewer website http://viewer.nationalmap.gov/viewer/
Zoom into area around the Gauge station
Click on the Download button on the Upper Right Corner

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Click on “Click here”, and draw a window around the target area, you have to eye ball a little to try to cover all of the streams you can see flowing towards the gauge station.

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Once the popup window opens select Elevation to download the DEM, you can also select Land cover
Hydrography for the target area if you need to. For this exercise we are only concerned with DEMs so just check Elevation and Click Next.

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The elevation data is available in various formats and resolutions, but we only need to download 1 arc second (30 m x 30m resolution), ArcGrid raster images. Sort the data by Resolution by clicking on the resolution column title and then check all the ArcGrid products corresponding to 1 arc second resolution.
Depending up on the area you have drawn a window across, you might have to download a few of these. After you have checked the boxes hit next and click check out on the left hand side of the map, fill in your information and you will be mailed a link to download the DEMs. DEMS are sent as Zip folders, you will need to unzip all the individual dems and add to ArcMap.

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You will notice all the DEMs have slightly different shades this is because each small DEM has an individual elevation scale, to work easy with we will have to put all of the DEMs in to a single DEM.
Search for Mosaic to New Raster tool

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Select all the DEMs you have and in the output location put the folder you want to keep the file in (Ex 5)
Put Number of Bands as 1 and hit ok, now you will get a nice map of the DEM, lets give it a nice color to make it attractive.
You can see that the Streams are running across the DEM, when you are doing watershed analysis make sure you have all the relevant DEM data included in the analysis. To make data processing fast we can reduce the size of the DEMS to what we need, you can see from the area draining into the Gauge station we can do without the area to the right and below the Palate River. Search for Extract by Rectangle tool
(You can do the similar thing with Clip tool, it gives you an additional option to clip by a set boundary like county, state or watershed).

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You should get something like this
Projecting DEM – Raster analyses such as watershed and stream network delineation are best performed in a consistent projected spatial reference system (or projection). This is because calculation of slope, length and area are involved and these are best done in linear (not geographic) units consistent with the elevation units. Let’s project the Clipped DEM into Albers Equal Area Conical projection.

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Now close the map and open a blank map and add the Projected DEM in to it, since it is in projected system it will look like this, you will observe a slight curvature in the DEM, this is because now we are in a projected coordinate system