This sentence has three important factors to consider: it is an existential construction, the displaced subject of the sentence is a noun phrase coordination, and the coordination is a list (more than two items).
In this particular case, is would be the safest choice (i.e., least likely to run afoul of any rules), although The Cambridge Grammar of the English Language suggests that are would also be acceptable, due to it being a list.
CGEL says either is or are is acceptable for your sentence.
Collins COBUILD states explicitly that is should be used.
From the Cambridge Grammar of the English Language (2002):
Typically the subject and verb should agree (pg 499).
There are however "semantically motivated overrides." One such override is when the subject is a coordination ("two or more elements of syntactically equal status... linked by means of a coordinator such as and or or"):
Ch 5, §18.4(a) Coordination with and
In general a subject with the form of a coordination of [noun phrases] linked by and takes a plural verb, as in Mary and John are here, etc. It doesn't matter whether the individual coordinates are singular or plural: the coordination as a whole here denotes a set containing at least two members, and hence takes a plural verb.
There are times though when "the subject is conceptualized as a single unit and this determines the singular verb." One of the examples given is, "Eggs and bacon is my favorite breakfast." In that particular example, "my favorite breakfast can only apply to eggs and bacon as a unit and hence the plural verb is impossible." (see also Ch15 §1.3.2 "Joint coordination", which discusses distributive vs. joint coordination in more depth)
The closest noun is however taken into account sometimes when using or (Ch 5 §18.4(b)) and always taken into account with a negative (Ch5 §18.4(d) and (e)).
The example you've given in the question though, is an existential construction (there is a "dummy pronoun" for the "displaced subject": rice, meat and tomatoes). (pg 241, Ch 4 §3.2.2)
Usually the verb should agree with the displaced subject (see footnote 71 on page 500):
There are tomatoes on my plate.
However, when the displaced subject is a coordination, there is an exception (footnote 21 on page 242). When the coordination consists of only two items (binary coordination) then it is idiomatic for the verb to agree with the first item in the list:
A further complication arises in existentials when the verb is followed by an NP-coordination, as in There was/?were a bottle of wine and several glasses on the table. Were tends to be unidiomatic with an NP-coordination when the coordinate that is adjacent to it is singular, even though the coordinate as a whole (a bottle of wine and several glasses) is plural.
A plural example is given on page 1393 [7i]:
There are good teachers and bad teachers.
The exception to the exception is when the coordination consists of a list (three or more items, aka multiple coordination). The last caveat in footnote 21 states that in such a case,
Plural agreement, however, occurs readily in lists: There are still Brown, Jones, Mason and Smith to interview.
Araucaria found an example on page 1400 demonstrating that a singular verb is also valid with lists (the use of "readily" in the footnote 21 is ambiguous about which is more common or preferred), [29i]:
A: Who was at the party last night? B: There was Mary, Sue, Fred, Matt and Sam.
So, with three items in your displaced subject (rice, meat and tomatoes), you can really choose either is or are (according to CGEL).
If there were only two items in the coordination, then it would be less ambiguous; a singular verb would be preferred/idiomatic. Also, note that a plural verb would not necessarily be ungrammatical, indicated by an asterisk, but merely questionable/unidiomatic, indicated by a question mark (see page xii for those notational conventions).
More information can also be found in Chapter 16 "Information packaging", section 6 "Existential and presentational clauses" on page 1390.
Collins COBUILD English Grammar states that with lists the verb should agree with the first item in the list.
10.50... You use a singular form of 'be' when you are giving a list of items and the first noun in the list is singular or uncountable.