The invitation letter should be polite in form. You should not start it with, "Hey, friend..." - not all the girls like simplicity of manners. To make it easier to suck it up and not to look for walking topic of conversation, it is best to offer a cultural programme that will be of interest to you both.
If you want to invite to walk a familiar girl, then you know something about her Hobbies. If you are not too close, check with mutual friends. Learn not is there somewhere an exhibition on the theme, which is interested in the girl: it can be decorative and applied art, photography or exhibition of purebred animals. If a girl decides that you have shared Hobbies, your chances of successful development of relationship it will grow. Can ask advice from a girl where to look for trained dogs or stone crafts, and invite her to go together.
If a girl likes sports, invite her to ski, Cycling, or on the tennis court or skating rink with artificial ice. On nature bring a thermos of tea or cold brew – the girl will appreciate your concern and foresight.
If you just met and shared friends you have, you can invite her to the movies after learning her preferences, to a disco or to a cafe. If it is difficult to decide on the invitation from the café, think - surely your city has some interesting sights. Invite the girl to go there. However, if you need to get on the road, warn her in advance that she shod accordingly – high heels is not comfortable. After the walk you can go to relax in the café it will be convenient and natural.
The man is unacceptable to be late for a meeting, it is assumed that the girl can afford a small delay.