Yes, it is entirely possible to have a beautiful garden that you can eat without looking like you have a vegetable garden in your front yard.
***Flowers from plants that have been chemically treated (especially pesticides) should be avoided.
Flowers to Avoid: Some flowers in particular to be avoided (but not a complete list) are: azalea, belladona lily, bleeding hearts, buttercups, cardinal flowers, clematis, cotoneaster, daffodil, fall crocus, foxglove, four-o’clock, hemlock, hyacinth, hydrangea, jack-in-the-pulpit, larkspurs, lily of the valley, lupine (some are edible, some are poisonous so use great caution), may apple (poisonous when green but good when yellow), narcissus, oleander, periwinkle, rhododendron, sweet peas, Virginia creeper, and wisteria. – Note: sources do not always agree on whether or not a particular plant/flower is poisonous. Some have been listed as poisonous with a notation that consuming large quantities is a problem, but not small quantities.
(The chart below is available as a pdf if you message me.)