Not exactly a date, but... shopping. Tell her you're going shopping for a certain thing on a Saturday day (and you actually are, even if window shopping), and that she's welcome to come along and choose places to make a stop as well. Plan to have lunch or coffee and snacks in the middle. Wander into a theater if it seems like the right thing to do.
In other words, spend some time together the way you and your eventual long-term love are most likely to -- shopping, hanging, talking, watching, improvising. With the right person, it's fun as hell.
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