search across models

hi all, i have a big question. 

how can i perform search queries like on following models

RESTAURANT_TYPES = (

    ('C', 'Chinese'),

    ('A', 'American'),

    ('J', 'Japanese'),

)    

class city (models.Model):

    name = models.CharField(max_length=200)

class restaurants(models.Model):

    name = models.CharField(max_length=456)

    city = models.ForeignKey(city)

    type = models.CharField(max_length=10, choices=RESTAURANT_TYPES)

    is_veg = models.BooleanField(default=True)

search queries:

1. restaurants in city1
2. city1 restaurants
3. Chinese restaurants
4. Chinese restaurants in city1
5. vegetarian restaurants in city1
6. vegetarian american restaurants
7. and so on...

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