The easiest, most out of the box solution to your problem is to create a text or choice field in your document library, and set it's default value based on whatever folder it's dropped in.
First you'll need a text/choice column to hold some data, then you configure location specific defaults by going to List Settings -> Column Default Value Settings, then select the location (folder) you want to configure. You'll set a corresponding value (something like the folder name) for each folder to your new column.
Now every time a document is uploaded, created, added in bulk (through explorer view, for instance), or created from an office program and saved to the location, the document will get the correct metadata value associated with the folder.
The major drawback here (other than those inherent in folder use) is that if a document is ever moved that text field won't be able to update itself, the person moving it will have to set it appropriately, which can be quite error prone.
Next easiest out of the box method is to make a workflow that fires on item creation which will write the 'Path' value (or one of the numerous other builtin URL item fields) to a metadata (text) field on your document items -- then filter a list view for files that are inside of that folder (via your new text field that contains the item URL) -- You can also make the workflow fire each time an item is edited if you want to make sure the path stays up to date as items are changed or moved.
The easiest, least amount of effort solution with SPD (assuming you understand some CAML) is to create the list view on the page then modify the list view web part's CAML query to filter only for items containing the URL you want, as wjervis suggested. You would need to filter on the FileRef field (or again, one of the many URL internal fields) -- if you create the list view in the browser and then filter a field with the contains operator that should get you most of the way there, you would just need to change the field info and the url string.
What I would do (without knowing all the specifics of your project/environment): You could also completely skip using folders, and use a choice/text field to categorize objects instead. Using metadata terms instead of folders is widely considered best practice for document management within SharePoint anyway, because it provides a number of other advantages in addition to making problems like this easier to manage.
You would avoid the hassle of working with variable URL paths, keep the ability to organize items in categories (use view grouping and it organizes your items just like how folders work), reduce the upkeep/possibility of duplicate files across your folders, and solve your initial problem of creating filtered views since you can quite easily filter on text/choice fields using normal list views.