Getting valid URL from user input
This piece:

if (fullUrl.EndsWith("/"))
{
    fullUrl += "Routes";
}
else
{
    fullUrl += "/Routes";
}


can be rewritten to:

fullUrl += fullUrl.EndsWith("/") ? "Routes" : "/Routes";


or:

if (!fullUrl.EndsWith("/"))
    fullUrl += "/";
fullUrl += "Routes";


Since you're using the TryCreate method, there's no need to throw an exception. You just have to notify the caller whether the conversion succeeded or not. Plus, throwing an exception in a get statement is bad practice. This results in following:

if (Uri.TryCreate(fullUrl, UriKind.Absolute, out uri))
    return uri.ToString();
//if no succesful creation:
return String.Empty;


If you do want to throw an exception, use a try/catch block and a regular Uri constructor. This should be placed in a method and not in the get statement then:

try
{
    uri = new Uri(fullUrl, UriKind.Absolute);
    return uri.ToString();
}
catch (UriFormatException ex)
{
    throw;
}


My favor would still be with the TryCreate resulting in following final code:

public string ServiceLocation
{
    get
    {
        var fullUrl = ConnectionStringData.Location.Trim();
        fullUrl += fullUrl.EndsWith("/") ? "Routes" : "/Routes";

        Uri uri = null;

        if (Uri.TryCreate(fullUrl, UriKind.Absolute, out uri))
            return uri.ToString();
        return String.Empty;
    }
}