From the south, the quickest route is probably to take the M1 northbound to junction 32, then the M18 eastbound to junction 2, the A1M northbound to junction 44 and finally the A64 eastbound to the York Outer Ring Road (A1237).
1	From	from	ADP	IN	_	3	case	3:case	Discourse=joint-other_m:44->11:5
2	the	the	DET	DT	Definite=Def|PronType=Art	3	det	3:det	Bridge=1<78|Entity=(78-place-acc:inf-cf3-2-sgl
3	south	south	NOUN	NN	Number=Sing	11	obl	11:obl:from	Entity=78)|SpaceAfter=No
4	,	,	PUNCT	,	_	3	punct	3:punct	_
5	the	the	DET	DT	Definite=Def|PronType=Art	7	det	7:det	Entity=(79-place-new-cf4-3-sgl
6	quickest	quick	ADJ	JJS	Degree=Sup	7	amod	7:amod	_
7	route	route	NOUN	NN	Number=Sing	11	nsubj:outer	11:nsubj:outer	Entity=79)
8	is	be	AUX	VBZ	Mood=Ind|Number=Sing|Person=3|Tense=Pres|VerbForm=Fin	11	cop	11:cop	_
9	probably	probably	ADV	RB	Degree=Pos	11	advmod	11:advmod	_
10	to	to	PART	TO	_	11	mark	11:mark	_
11	take	take	VERB	VB	VerbForm=Inf	0	root	0:root	_
12	the	the	DET	DT	Definite=Def|PronType=Art	13	det	13:det	Entity=(80-place-new-cf5-2-coref-M1_motorway
13	M1	M1	PROPN	NNP	Number=Sing	11	obj	11:obj	Entity=80)
14	northbound	northbound	ADJ	JJ	Degree=Pos	13	amod	13:amod	_
15	to	to	ADP	IN	_	16	case	16:case	_
16	junction	junction	NOUN	NN	Number=Sing	11	obl	11:obl:to	Entity=(81-place-new-cf9-1-sgl
17	32	32	NUM	CD	NumForm=Digit|NumType=Card	16	dep	16:dep	Entity=81)|SpaceAfter=No
18	,	,	PUNCT	,	_	21	punct	21:punct	_
19	then	then	ADV	RB	PronType=Dem	21	advmod	19.1:advmod	_
19.1	take	take	VERB	VB	VerbForm=Inf	_	_	0:root|11:conj:and	CopyOf=11
20	the	the	DET	DT	Definite=Def|PronType=Art	21	det	21:det	Entity=(82-place-new-cf6-2-sgl-A18_road_%28England%29
21	M18	M18	PROPN	NNP	Number=Sing	11	conj	19.1:obj	_
22	eastbound	eastbound	ADJ	JJ	Degree=Pos	21	amod	21:amod	Entity=82)
23	to	to	ADP	IN	_	24	case	24:case	_
24	junction	junction	NOUN	NN	Number=Sing	21	orphan	19.1:obl:to	Entity=(83-place-new-cf10-1-sgl
25	2	2	NUM	CD	NumForm=Digit|NumType=Card	24	dep	24:dep	Entity=83)|SpaceAfter=No
26	,	,	PUNCT	,	_	28	punct	28:punct	_
26.1	take	take	VERB	VB	VerbForm=Inf	_	_	11:conj:and	CopyOf=11
27	the	the	DET	DT	Definite=Def|PronType=Art	28	det	28:det	Entity=(84-place-new-cf7-2-sgl-A1_road_%28Great_Britain%29
28	A1M	A1M	PROPN	NNP	Number=Sing	11	conj	26.1:obj	_
29	northbound	northbound	ADJ	JJ	Degree=Pos	28	amod	28:amod	Entity=84)
30	to	to	ADP	IN	_	31	case	31:case	_
31	junction	junction	NOUN	NN	Number=Sing	28	orphan	26.1:obl:to	Entity=(85-place-new-cf11-1-sgl
32	44	44	NUM	CD	NumForm=Digit|NumType=Card	31	dep	31:dep	Entity=85)
33	and	and	CCONJ	CC	_	36	cc	36:cc	_
34	finally	finally	ADV	RB	Degree=Pos	36	advmod	34.1:advmod	_
34.1	take	take	VERB	VB	VerbForm=Inf	_	_	11:conj:and	CopyOf=11
35	the	the	DET	DT	Definite=Def|PronType=Art	36	det	36:det	Entity=(86-place-new-cf1-2,6,7,8,9-coref-A1237_road
36	A64	A64	PROPN	NNP	Number=Sing	11	conj	34.1:obj	_
37	eastbound	eastbound	ADJ	JJ	Degree=Pos	36	amod	36:amod	_
38	to	to	ADP	IN	_	43	case	43:case	_
39	the	the	DET	DT	Definite=Def|PronType=Art	43	det	43:det	Entity=(87-place-new-cf8-2,3,4,5-coref-York_Outer_Ring_Road
40	York	York	PROPN	NNP	Number=Sing	43	compound	43:compound	Entity=(1-place-giv:act-cf2*-1-coref-York)
41	Outer	Outer	ADJ	NNP	Degree=Pos|Number=Sing	42	amod	42:amod	_
42	Ring	Ring	PROPN	NNP	Number=Sing	43	compound	43:compound	_
43	Road	Road	PROPN	NNP	Number=Sing	36	orphan	34.1:obl:to	Entity=87)86)
44	(	(	PUNCT	-LRB-	_	45	punct	45:punct	Discourse=restatement-partial:45->44:0|SpaceAfter=No
45	A1237	A1237	PROPN	NNP	Number=Sing	43	appos	43:appos	Entity=(86-place-giv:act-cf1-1-coref-A1237_road)|SpaceAfter=No
46	)	)	PUNCT	-RRB-	_	45	punct	45:punct	SpaceAfter=No
47	.	.	PUNCT	.	_	11	punct	11:punct	_
