Urban = city or ‘spaces dominated by buildings’.
Peri-urban = village/towns/suburbs or ‘spaces with a balance of building and landform’.
Rural = sparsely developed or ‘few if any buildings’.

As well as a character distinction. So:

Character = essence/mood or atmosphere.

Urban landscape = large scale spaces in which an urban landscape character is evident.
Rural landscape = large scale spaces in which a rural landscape character is evident.

OK, so for landscape do you want to make a distinction between landform (with any quality) and landscape (of a high quality)?

The links provided are only giving text responses. So to the BUT, BUT, BUT…

I like the use of examples, and am not aiming to be pernickity, but I do think examples need coupling to definitions. Your example of ‘peri-urban landscape’ contains both urban and landscape character. Could the definitions you are implying be:
urban = small-scale spaces dominated by buildings
rural= few, if any, buildings
urban landscape= large-scale spaces in which landform is evident
Getting back to Copenhagen, I think my point is that the Green Fingers should have been ‘almost rural’ (as the Green Wedges are) and the Robert’s point (above) is that they although they are urban they have some internal greenery.
On the question of ugly/beautiful, I think the word ‘landscape’ has a positive connotation when applied to space within cities. It is a bit like the distinction between a ‘building’ (which can have any quality) and a ‘work of architecture’ which is intended to be high quality (even if tastes differ).
Here is one of my favourite examples of a Green Finger (though Copenhagen is a little flat to create this effect!)
http://www.henniker.org.uk/images/places/local_a/stockbridge/st_bernards_well.jpg
http://www.henniker.org.uk/images/places/local_a/dean_village/RandolphCresc02.jpg
http://www.henniker.org.uk/images/places/local_a/queensferry_rd/dean-bridge06viewdownstream.jpg

However, any particular instance can be described (by good, bad, ugly or beautiful).

Examples of a peri-urban character are:

[ http://scotterb.files.wordpress.com/2010/05/may26-069.jpg ]

Examples of peri-urban landscape character are:

[ http://www.english-heritage.org.uk/content/images/coastal-marine-wrecks/overlooking-the-town-and-harbour ]

Instances of rural character are:

[ http://www.prairiemod.com/.a/6a00d8341bf72a53ef0120a56e0496970c-300wi ]

Instances of rural landscape character are:

[ http://www.discounthotelsavings.com/hyatt/images/hyatt-regency-hotel-scottsdale-arizona-1.jpg ]

California modern relied considerably on urban landscape character [ http://have2ask.com/files/images/CM05.preview.jpg ] and rural landscape character [ http://arquitecturainteligente.files.wordpress.com/2007/11/kaufman_house_palm_springs.jpg ], (but not entirely see Interiors [ http://www.shorpy.com/files/images/CM01.preview.jpg ]).

Although there is much blurring, ‘urban’ and ‘rural’ have distinct meanings and ‘urban character’ is the character of an ‘urban’ area. But I do not think this answers the question of what ‘urban landscape character’ means. I think the four main candidates are as listed below and I think I favour ‘2)’:
1) any outdoor space in a city
2) a good quality outdoor space in a city
3) a vegetated outdoor space in a city
4) an un-bounded outdoor space in a city

Here are three examples which should be easy to guess…1) [ http://www.poszu.com/wp-content/uploads/2011/07/real-hutong.jpg ] 2) [ http://www.helveticafilm.com/images/melbourne5.jpg ] 3) [ http://janesguidetoscotland.com/wp-content/uploads/2010/05/city-centre-glasgow.jpg ]

So in this sense ‘Urban landscape character’ [ http://www.concierge.com/images/destinations/destinationguide/australia_pacific/australia/melbourne/melbourne/melbourne_013p.jpg ] describes something of the ‘urban geography’ and how it informs the ‘urban character’.

Interesting about Nelson. In English folklore, he is famed for disobeying orders with the implication that the bureaucrats are over-bound by regulations and our hero is set on ignoring them so that he can get the job done.
Which Urban Landscape Conference are you referring to? I find urban landscape a very useful term, suggesting (a little like Ebenezer Howard’s Three Magnets Diagram) a place which combines the excellencies of tows with the excellencies of the landscapes which are found outside towns. Also, as you say, it implies consideration of outdoor space at multiple scales. Geogre Hargreaves gave an interesting account of his work at the University of Cincinatti and one of the points he made was that the central part of the campus should have an ‘urban character’. I do not remember him using the concept of Landscape as a design objective for the campus but I think one of the less-strong points of his general design approach is the treatment of broad landscapes. An exception to this was his design for Crissy Field by the Golden Gate Bridge in San Francisco. There, he spoke lyrically about the wonderful views and, correctly, did nothing to make the place fussy. It is and was a place to appreciate a very large-scale urban landscape.

Parker would have been able to see little of the battle owing to gun smoke, though he could see the signals on the three grounded British ships, with Bellona and Russell flying signals of distress and the Agamemnon a signal of inability to proceed.[11] Thinking that Nelson might have fought to a stand-still but be unable to retreat without orders (the Articles of War demanded that all ranks do their utmost against the enemy in battle), at 1:30pm Parker told his flag captain, “I will make the signal of recall for Nelson’s sake. If he is in condition to continue the action, he will disregard it; if he is not, it will be an excuse for his retreat and no blame can be imputed to him.”

I am in favour of what could possibly be called the urban landscape approach (borrowed from the Conference definition of Urban Landscape.)

Urban Landscape as a term is used here, in its broadest sense, to describe and interpret changing landscapes of cities and towns. The examples employed in this study include urban landscapes on a neighbourhood scale, on a city scale, and on a regional scale. The “urban landscape” concept assumes that these levels should be considered, not separate from each other, but together and simultaneously.

It is worth considering the urban landscape on the three scales 1) neighbourhood 2) city and 3) regional, because each scale will tell you something different about planning considerations and possible design strategies.