Answer: Citrus trees (orange, tangerine, lemon , lime, etc. will grow well in Palm Springs, as will:
Apricot trees (Prunus family) reach 15 to 20 feet in height and have pink or white blooms in Spring. Varieties that do well in the desert are: 'Early Gold', 'Blenheim', 'Royal', 'Chinese', 'Tilton', 'Floragold' (a dwarf variety), and 'Newcastle'. Most of these are self-pollinating and need some winter chill.
Plum trees (Prunus) reach 10 to 15 feet in height and will need a winter chill period to produce abundant fruit. Among the best varieties for our hot, dry climate are two self-pollinators: 'Beauty' and 'Santa Rosa'. The 'Satsuma'. 'Burbank', 'Howard Miracle', 'Mariposa' and 'Friar' can be pollinated by the 'Santa Rosa'. There are, of course, the ornamental plums, but why grow them when you can grow fruit bearing trees?
Nectarine trees (Prunus persica nucipersica) need to be pruned back severely every year because the fruit grows only on the first year growth. Even then you are likely to have a bumper crop annually. Plant these self-pollinating varieties: 'Goldmine', 'Gower', 'Stanwick', and 'Le Grand' and you can feed the whole neighborhood.
Peach trees (Prunus persica) as well as nectarine trees grow to about 25 feet high, if left unpruned. Pruning is recommended to keep tree height to under 12 feet. They will start producing fruit in about 3 or 4 years and you can place 2 or 3 varieties in one hole when you plant. Some varieties that do well in the desert are: 'Desert Gold', 'Early Elberta', 'Bonita', and 'Rio Grande'. The following are dwarf trees: 'Bonanza II', 'Southern Sweet', and 'Southern Flame'.
Figs (Ficus carica) are big leaf trees that grow fast to 15 to 30 feet in height. They love the heat and do well when planted near a south-facing wall -- but not too close. Eventually the tree trunk becomes quite large. Most varieties produce 2 crops a year and, for home garden use, do not need another fig tree to for pollination. The best varieties for the desert are: 'Black Mission', 'Kadota' and 'Brown Turkey'.
You can also grow Pomegranate (Punicaceae). It grows as a rounded shrub that reaches 8 feet in height and is self-fruitful. These can make an edible hedge if you plant them about 4 feet apart. The best variety to plant is the 'Wonderful'. Pomegranates can take all day sun and will grow in alkaline soil.
I'm afraid apples won't do well in Palm Springs - they need a pronounced winter chill which is something the region just can't provide.
Best wishes with your edible garden!
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